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Rubber Fatigue ≠ Metal Fatigue Part 3: Thermal Effects

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All materials are temperature dependent, but some more than others: metals tend to be crystalline solids and will melt at sufficiently high temperatures; in contrast, crosslinked elastomers are always solids. They can be glassy or rubbery, crystalline or amorphous. When heated to extreme temperatures, they burn rather than melt, producing new substances, usually low molecular weight hydrocarbons (i.e. tarry substances and smoke).

Of course, you do not have to melt or burn a material to see the effects of temperature. In fatigue analysis, we are concerned with stress-strain and crack growth behaviour. These can be temperature dependent for both metals and rubbers. However, while metals have a very high thermal conductivity, rubbers have almost the lowest. Therefore, fatigue analyses involving large temperature gradients are much more common in rubber than in metal.

As shown in Fig.1, while a 100°C temperature gradient in a metal can affect the fatigue tensile strength or the fatigue limit by 10% [1], the same 100°C temperature gradient in rubber can reduce the fatigue life by four orders of magnitude [2]!

Fig. 1. Left – Effects of temperature on carbon steel showing tensile strength (+), yield stress (●), and fatigue limit (○), [1]; Right – Effects of temperature on natural rubber (Δ) and styrene butadiene rubber (●) [2].
Temperature and Segmental Mobility

The mechanisms underlying the elasticity of metals and rubbers could hardly be more different.  Under stress, atoms in a metal’s crystal lattice are displaced from their equilibrium positions, and potential energy is stored in strained interatomic bonds.  In rubber, however, the strain energy is not predominantly stored in strained atomic bonds.  Rather, elasticity arises because the constituent long-chain molecules are much more likely to be randomly coiled than to be fully extended.

Thus, provided that the molecules are sufficiently agitated by random thermal fluctuations, an entropic spring effect is created, meaning that potential energy can be stored by working to reduce the entropy of the polymer chain network by increasing the end-to-end distance of individual polymer chains [3].

Polymers in general can exhibit both glassy and rubbery behavior, depending on the temperature.  The rubbery state – in which entropic elasticity dominates – exists above the glass transition temperature Tg, if the molecular motion rate is sufficiently high.  In the rubbery state, very large strains are possible and the rubbery elastic storage modulus E’r determines the stress-strain curve.

Below Tg, however, the lack of thermal molecular mobility prevents molecular reconfiguration, resultng in a glassy stiffness E’g that is several orders of magnitude higher than E’r.  Polymers operating below Tg are thus not capable of large elastic strains and instead exhibit inelastic behavior when strains exceed a few percent.  Figure 2 shows how the storage and loss moduli vary through the glass transition (left), and how the rate of molecular motion rate depends on temperature (right).  The relative rate φ(T)/φ(Tg) of molecular motion as a function of temperature T is described by the WLF equation [4], which has material constants A and B.

Since the fracture mechanical properties of rubber depend on the viscoelastic dissipation in the crack tip process zone, with higher dissipation associated with lower crack growth rates, frequency and temperature effects can be inferred accordingly. Viscoelastic master curves, such as those shown in Fig. 2, can be used as part of the material property rate dependence specification in the Endurica solver.

Fig. 2, Left – Rubber’s elastic and viscous responses depend on temperature relative to the glass transition temperature Tg; Right: The rate of molecular motion depends on temperature relative to the glass transition temperature Tg.

Self-Heating and Thermal Runaway

During a charge cycle, work WL is done on the charge stroke, some of which WU is recovered on the discharge stroke, as shown in Fig. 3.  The unrecovered part of the work H remains in the material as heat energy, increasing the temperature.

 

Fig. 3. Work input WL on the loading stroke is partially recovered as WUon the unloading stroke. A portion H of the energy remains in the material as heat.

The rate of viscoelastic heating of rubber depends on strain amplitude, cycle rate (i.e. frequency) and temperature. The strain amplitude dependence of the viscoelastic storage and loss modulii, G’ and G” respectively, can be specified using the Kraus model [5,6]:

 

where εa is the strain amplitude, and where G’∞, G’0, εa,c, m, G”∞, G”max, and ΔG”U are material parameters. The viscoelastic heat rate per unit volume can be calculated from:

Due to the low thermal conductivity of rubber, small amounts of viscoelastic self-heating can produce large temperature gradients.  Accurately accounting for thermal effects on rubber durability generally requires both structural finite element analysis to calculate stress and strain fields, and a thermal finite element analysis to calculate the temperature field. Endurica fatigue solvers can provide heat rate calculations in a coupled finite element simulation for both transient and steady state thermal analyses.

In cases where the temperature in the rubber exceeds a critical value Tx, an additional heat rate contribution q ̇x occurs due to exothermic chemical reactions.  The effect is illustrated in Fig. 4, for a rubber cylinder subjected to a rotating bending load [7]. The thermal runaway starts after about 250 seconds. Both experimental (dashed line) and Endurica-calculated (solid line) simulation results are plotted for the cylinder centreline (blue) and for the cylinder outer surface (green).  The thermal runaway event typically results in rapid decomposition of the rubber into hydrocarbon gases (i.e. smoke/burning rubber) and low-molecular weight substances (tar).

Fig. 4. When temperature exceeds a critical value Tx, exothermic chemical reactions can produce a thermal runaway failure. Plot (right) shows Endurica calculated transient temperature history (solid lines) for a rotating bending cylinder (structural finite element model shown on left). For comparison, experimentally measured temperature histories are also shown (dashed lines).

Reversible Temperature Effects

The crack growth properties of rubber reversibly depend on temperature.  Higher temperatures tend to reduce the tear strength Tc  of rubber and increase the crack growth rate, as shown in Fig. 5 [8].  At lower temperatures, the tear strength is increased and crack growth is retarded.  Endurica’s crack growth models can be specified with a temperature dependence via the temperature sensitivity coefficient (see Table 1) or via a table look-up function.

Fig. 6 shows the fatigue life as a function of temperature calculated from the parameters in Table 1 [2].  Over a range of 100°C, natural rubber loses approximately a factor of two in fatigue life, and styrene butadiene rubbers loses four orders of magnitude!

Table 1. Crack growth properties and temperature sensitivity for natural rubber (NR) and styrene butadiene rubber (SBR), estimated from measurements reported in [2].
Fig. 5 – Increasing temperature causes the crack growth rate to increase. Results are shown for natural rubber [8].
Fig. 6. Endurica calculated dependence of fatigue life on temperature for natural rubber (Δ) and for styrene butadiene rubber (●) [2]. Compare to Fig. 1.
Some rubbers undergo strain crystallization, which is beneficial when operating under non-relaxing conditions.  The crystallization effect is strongly temperature dependent and decreases with increasing temperature.

Fig. 7 shows the Haigh diagram calculated by Endurica for three different temperatures: 23, 90 and 110°C.  For example, at a mean strain of 100% and a strain amplitude of 20%, the fatigue life at 23°C exceeds 106 cycles, but at 110°C the fatigue life is approximately 103 cycles.  This effect has been confirmed experimentally in recent work by [9].

Fig. 7. Endurica calculated Haigh diagrams for natural rubber at 23, 90 and 110°C . Increasing temperature tends to reduce strain crystallization, with the result that the mean strain benefit associated with strain crystallization is reduced or even eliminated at high temperatures.

Irreversible Temperature Effects / Ageing

Prolonged exposure to high temperatures can cause permanent changes in the cross link density and mechanical properties of rubber, including stiffness and crack growth properties.  The effect depends on the availability of oxygen [10], as shown in Fig. 8.

Fig. 8 – The evolution of rubber’s properties during ageing depends on the availability of oxygen, and on the temperature [10]. Under aerobic conditions, ageing tends to increase stiffness while strain at break decreases. Under anaerobic conditions, ageing tends to decrease stiffness while strain at break decreases.
When aged under Type I aerobic conditions, rubber becomes brittle as its strain at break λb decreases while its stiffness M100 increases.  When aged under Type II anaerobic conditions, rubber tends to soften while its strain at break decreases.

The rate at which thermochemical ageing of rubber progresses can be specified in Endurica using the Arrhenius law [11] and its activation energy parameter Ea. When following a temperature history θ(t), Endurica integrates the Arrhenius law to determine an equivalent exposure time τ at the reference temperature θ0.  R is the real gas constant.

The equivalent exposure time controls the evolution of the stiffness and crack growth properties with thermal history. As shown in Fig. 9, the evolution of the crack growth rate law is specified by a tabular function that gives the stiffness E(τ), tensile strength Tc(τ) and the fatigue limit T0(τ).  The material properties are then updated iteratively according to the co-simulation workflow shown in Fig. 10.  This allows the effects of thermal history and ageing on fatigue performance to be considered.

Fig. 9. The crack growth rate law evolves as a function of the equivalent exposure time τ. Crack growth property evolution is specified in Endurica by the dependence of the rubber’s tear strength Tc(τ) and its fatigue limit T0(τ) on exposure time.

 

Fig. 10. Endurica DT’s co-simulation workflow updates the crack length c, exposure time τ, and stiffness E so that stress, strain and temperature fields can be updated during solution.

Conclusion

There are many ways in which metals and rubbers differ in their behaviour, and thermal behaviour is one of the most important.

Rubber more often requires careful attention to thermal effects due to its exceptionally low thermal conductivity, its entropy-elasticity, its visco-elastic properties and tendency to self-heat under cyclic loading, the sensitivity of crack growth properties and strain crystallization to temperature, oxidation, and ageing.

Endurica’s fatigue solvers provide material models and workflows that capture these thermal effects, enabling accurate analysis and “right the first time” engineering.

References

[1] P.G. Forrest, Fatigue of Metals, Pergamon Press: Oxford, New York, 1962.

[2] G.J. Lake and P.B. Lindley, “Cut growth and fatigue of rubbers. II. Experiments on a noncrystallizing rubber”, Journal of Applied Polymer Science, vol. 8(2), pp. 707-721, 1964.

[3] W. V. Mars and T. G. Ebbott, “A Review of Thermal Effects on Elastomer Durability” in Advances in Understanding Thermal Effects in Rubber: Experiments, Modelling, and Practical Relevance, G. Heinrich, R. Kipscholl, J. B.
Le Cam and R. Stoček (eds.), pp. 251–324, Springer Nature: Switzerland, 2024.

[4] M. L. Williams, R. F. Landel and J. D. Ferry, “The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-forming Liquids”, Journal of the American Chemical Society, vol. 77 (14), pp. 3701–3707,
1955.

[5] G. Kraus, “Mechanical Losses in Carbon Black Filled Rubbers”, in: Journal of Applied Polymer Science: Applied Polymer Symposium, vol. 39, pp. 75–92, 1984.
[6] J. D. Ulmer, “Strain Dependence of Dynamic Mechanical Properties of Carbon Black-Filled Rubber Compounds”, Rubber Chemistry and Technology, vol. 69, pp. 15–47, 1996.

[7] J. Vaněk, O. Peter et al, “2D Transient Thermal Analytical Solution of the Heat Build-Up in Cyclically Loaded Rubber Cylinder” in Advances in Understanding Thermal Effects in Rubber: Experiments, Modelling, and Practical Relevance,
G. Heinrich, R. Kipscholl, J. B. Le Cam and R. Stoček (eds.), pp. 31–52, Springer Nature: Switzerland, 2023.

[8] D. G. Young, “Fatigue Crack Propagation in Elastomer Compounds: Effects of Strain Rate, Temperature, Strain Level, and Oxidation”, Rubber Chemistry and Technology, vol. 59 (5), pp. 809–825, 1986.

[9] B. Ruellan, J. B. Le Cam et al, “Fatigue of natural rubber under different temperatures”, International Journal of Fatigue, vol. 124, pp. 544–557, 2019.isms in amorphous polymers and other glass-forming liquids. Journal of the American Chemical society, 77(14), 3701-3707.

[10] A. Ahagon, M. Kida and H. Kaidou, “Aging of Tire Parts during Service. I. Types of Aging in Heavy-Duty Tires”, Rubber Chemistry and Technology, vol. 63 (5), pp. 683–697, 1990. [11] S. Arrhenius, “Über die Reaktionsgeschwindigkeit bei der Inversion von Rohrzucker durch Säuren”, Zeitschrift für Physikalische Chemie, vol. 4 (1), pp. 226–248, 1889.

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4-in-1

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Wow – this year has really been one of many firsts for Endurica.  We had our first ever Community Conference in April, we started our first sister company – in Europe, and from September 9 – 13, 2024, we presented 4 technical papers – a new Endurica record for one week!  The other impressive aspect of this latter feat was that the four presentations were on vastly different topics! I’ll just list the venues and titles and then discuss each one.

International Elastomer Conference 2024, Pittsburgh, PA, USA:

  1. “Heat Build-Up and Thermal Runaway in a Rotating Bending Experiment”

44th Annual Meeting and Conference of The Tire Society, Akron OH, USA:

  1. “Coupled Multiphysics Strategy to Monitor the Health of Rubbery Structures Using Endurica Tools”
  2. “Critical Plane Analysis of Surface-proximal Fields for the Simulation of Mechanochemical Wear”
  3. “Models, Materials and the Move Towards Virtual Product Development”

Let’s start with the first presentation on heat build-up. Will Mars presented this paper at the IEC in Pittsburgh on Tuesday the 10th of September. The presentation highlighted a new machine that has been developed by Coesfeld to evaluate the heat build-up behavior of rubber compounds. It uses a hollow rubber tube that is bent to a 60-90 degree arc and then rotated at about 600 rpm to create a tension-compression cycle throughout the tube due to the pre-bending as shown below.

This test offers many advantages over the historical Goodrich Flexometer self-heating test originally developed in 1937.  The Heat Build-Up Analyzer is instrumented to measure internal temperature as well as forces and deformations while the test is progressing.  The recent advances in the Endurica software and workflows are also equipped to predict the transient behavior in this test.  When the rubber reaches a certain high temperature, the rubber starts to break down, often due to the volatilization of low molecular weight additives creating an exothermic reaction, and also due to the reversion of the cross-links.  The exothermic reaction and thermal “runaway” condition can also be predicted by Endurica software.  The animation below shows the elevated temperatures and the internal pressure rise due to the exothermic reactions. The combination of the HBA test and the Endurica FEA-based analysis will add understanding to the heat-rise behavior of compounds for any company.  As with some other Coesfeld machines, Endurica is the sole distributor in the Americas.

The second presentation listed was presented by Mahmoud Assaad, co-authored by others at Endurica and also by Ed Terrill at ARDL.  This work aims to provide the combination of a full oxygen diffusion and oxidation reaction simulation and experimental characterization capability.   The plot here shows the distribution of reacted oxygen in the crown area of a commercial truck tire.  As the oxygen diffuses into the carcass it also reacts with the rubber compounds creating a phenomenon known as Diffusion Limited Oxidation.  Mahmoud, Ed Terrill and I worked on rubber oxidation with Sandia National Laboratories when the three of us worked together at Goodyear. Now we have developed a characterization and simulation capability that should be ready for customers to try in 2025!

For the third presentation listed, Will Mars quickly travelled from the IEC in Pittsburgh to the Tire Society in Akron to give a talk on an evolving capability for wear prediction. This work was co-authored by Lewis Tunnicliff and James Kollar at Birla Carbon as well as others from Endurica. For many years, researchers have been trying to link rubber fracture and tearing behavior to surface wear. One of the early works on this topic is shown in the drawing below from Southern and Thomas in 1979.

This work attempted to explain observations from blade abrader experiments. The Endurica/Birla work broadens this concept to different asperity shapes and a cumulative fatigue process that depends on the depth into the surface.  Temperature distribution near the surface was also calculated and included in the analysis.  Initial results gave similar trends for wear rates as work done by Gent and Pulford in 1983.  This new approach also makes it easy to also incorporate any aging effects that may occur on the surface of a rubber product. Development work on this new capability will continue well into 2025. In the meantime, Endurica does have a more basic FEA-based offering for wear prediction that has been used for multiple customers.

Lastly, on Friday the 13th of September, I had the honor of giving the Plenary Lecture for the Tire Society conference.  Thanks go to Jim McIntyre and the conference organizers for giving me this unique opportunity to address the society.

In April, we conducted the first ever Endurica Community Conference, and we tied in the Solar Eclipse that passed over Findlay, Ohio on April 8th, to produce a very successful event.  I wanted to include the solar eclipse in my Plenary talk and somehow relate it to topics concerning the development of tires.  The two concepts I used to make the connection were:

  • All models are approximations, but some can be very useful, and
  • Some very good physics theories predict singularities. The singularities reveal our ignorance on the topic and show the area where further work and insights are needed.

The first concept comes from the late George E. P. Box, a statistics professor at the University of Wisconsin. The quote is usually stated as: “All models are wrong, but some are useful”. The second concept makes a tie between fracture mechanics and Einstein’s General Theory of Relativity, which was validated by data taken during a solar eclipse in 1919. Both of these theories predict non-physical singularities but remain extremely useful.

The bulk of my talk was on Virtual Tire Development using tire durability as one of the performances to evaluate without building and testing prototypes. It largely followed my experience and contributions to the topic over the 3+ decades I worked on this at Goodyear with many excellent colleagues and partner organizations like Sandia.

All four of these presentations are available on our website at this location: Fatigue Ninja Frontier – Resources from Endurica’s First Annual Meeting.

Please contact us if you have any questions about these presentations or if you would like to chat with us about anything, including possible work together.

One final note: we are working on a revised website. Our Marketing Director, Pauline Glaza, is heading up a project to develop a new website for us that should make navigating our material and interacting with us much easier.  Expect to see our new site in early 2025!

 

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Rubber Fatigue ≠ Metal Fatigue Part 2: Linear Superposition

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Rubber Fatigue DOES NOT EQUAL Metal Fatigue Part 2 Linear Superposition

The load cases to be considered in fatigue analysis can be very lengthy and can involve multiple load axes. Often, load cases are much longer than can be calculated via direct time-domain finite element analysis (FEA).

In metal fatigue analysis, linear superposition is a widely used technique to generate stress-strain history from road loads [1], [2], [3]. When structures behave linearly, this approach is accurate and computationally efficient, allowing the analysis of lengthy load signals. For single axis problems, the finite element (FE) solution for a single unit load case is simply scaled according to the input load history. For multiaxial problems, unit load cases are solved for each of the axes, then scaled and combined according to the input load history.

Due to rubber’s 1) nonlinear material behaviour, 2) nonlinear kinematics, and 3) the possibility of nonlinear contact, linear superposition cannot be applied to rubber fatigue analysis. This article is the second in a series examining how rubber fatigue analysis procedures differ from those used for metal fatigue. Here we present the Endurica EIETM (Endurica Interpolation Engine) solver, which is a tool for the rapid generation of stress-strain histories for fatigue analysis in cases where linear superposition fails.

Nonlinearity figures in the analysis of rubbery materials in several ways including material nonlinearity, kinematic nonlinearity, and contact linearity. Endurica’s EIE solver provides an efficient and accurate method for generating stress-strain history when there is strong nonlinearity.
Fig.1. Nonlinearity figures in the analysis of rubbery materials in several ways including material nonlinearity, kinematic nonlinearity, and contact linearity. Endurica’s EIE solver provides an efficient and accurate method for generating stress-strain history when there is strong nonlinearity.

Brief review of the linear superposition procedure for metals

For linear structures, the relationship between forces [F] and displacements [u] can be written as a matrix multiplication where [k] is the stiffness matrix.

[F] = [k][u]

The associative property of function composition means that multiplying the displacements by a scalar a produces proportionally larger forces.

a[F] = [k](a[u])

The distributive property of addition means that a force system resulting from combined displacements [u] and [v]

[F] = [k][u] +[k][v]

can also be calculated as

[F] = [k]([u] + [v])

Similarly, stress and strain fields can be scaled and combined by linear superposition. Engineers have been using this principle for many years in metal fatigue analysis, particularly for treating multiaxial cases arising from field-recorded load-displacement histories.

The stress and strain fields in a part are assumed to result from a linear combination of unit load cases, where the scale factor for each unit load case is applied to the stress or strain field corresponding to a given input channel.

For example, for the beam shown in Fig.2, if channel 1 is the unit displacement u with magnitude a(t), and channel 2 is another unit displacement v elsewhere in the structure with magnitude β(t) , then the entire history of stress and strain at all points in the beam can be recovered by linear superposition.

Note that the FE solver only needs to produce a single time-independent solution for each unit load case. The time dependence of the solution is obtained entirely through the time variations of the scale factors a(t) and β(t). This extremely efficient method has been used for many years in metal fatigue analysis. It allows rapid analysis of complete road load histories consisting of millions of time steps.

Linear superposition of single load case FE solutions has long been used to generate stress-strain histories from road load histories in metal fatigue analysis.
Fig.2. Linear superposition of single load case FE solutions has long been used to generate stress-strain histories from road load histories in metal fatigue analysis.

Endurica EIETM: load space discretization and interpolation for nonlinear cases

Solving the nonlinear case requires a completely different approach. We wish to retain the advantages of efficiently constructing stress-strain time histories from precomputed FE solutions. Instead of precomputing a single unit load case for each input channel, we precompute a set of load cases from a discretized load space. We call this set a map.

The number of load cases in the map must be sufficient so that we can use interpolation to obtain an reasonable approximation of the nonlinear response at any point within the map. Fig.3 shows a map with two channels defined by x and z displacements. The blue points in the map are precalculated using an FE solver such as Ansys or LS-Dyna following the path traced by the blue line. Once the map is defined, the stress-strain history along the red line can be interpolated from the precomputed solutions in the map.

Endurica EIE discretization map
Fig.3. Two-channel map discretizing a space defined by the x and z displacements. Blue dots represent FE solutions for which the stress-strain fields are precomputed. The blue line represents a solution path, which defines the order in which the solutions are computed and stored in the results database. The red line represents a possible actual displacement history. The stress-strain history for points on the red path is obtained by interpolation from points on the precomputed map.

Endurica EIETM is a general purpose tool for creating and using non-linear maps to generate stress-strain histories for fatigue analysis [4], [5]. EIE is an abbreviation for efficient interpolation engine. EIE provides a simple workflow and powerful utilities for creating and using maps for interpolation. It supports up to six independent input channels.

The entire EIE workflow consists of three main steps. The first step is to create a map. The next step is to specify your history in terms of forces or displacements. Note that any quantity that can be applied as a boundary condition to the FE model can be set up as a channel. The last step is to perform the specified interpolation. The process produces a time history of strain tensor components for each element in your FE model.

The map creation process involves four steps, as shown in Fig.4. First, the number of independent channels that will be used to specify the history must be defined. The map type must also be specified. Several types are available, including a completely customizable map. Grid-based maps are often appropriate for one-, two- and three-dimensional maps. For higher dimensional maps, case vector-based maps are often the most convenient.

Once the map type has been defined, EIE generates solution paths. These consist of enumerated load states that should be applied as boundary conditions to the FE model to generate the map. One or more paths may be generated depending on map type. Each path is called a branch. For each branch, EIE writes a file with the appropriate boundary condition history, which is necessary for the generation of the map. Next, the FE model is set up and executed using EIE’s boundary conditions. Finally, the database of FE results is linked to the corresponding branch in the definition of the map.

At this point the map is complete and ready for interpolation. Note that linear superposition can be implemented as a special case in EIE when unit load case solutions are collected and defined as a map. In general, however, a non-linear map will contain a greater number of solution steps.

 

Steps to specify a map for use by Endurica EIE.
Fig.4. Steps to specify a map for use by Endurica EIETM.

Specifying the load history is as simple as selecting a file containing the time history of each input channel. In the file, each row represents one time step and each column represents an input channel. EIE supports .csv and .rsp formats, both common data formats. Fig.5 shows an example history with  and  displacements. Note that the range of displacements in the history should not exceed the range of the precalculated map. Although interpolated solutions can be quite accurate, extrapolation for non-linear problems can be very risky and inaccurate.

Endurica example of two-channel displacement history for interpolation
Fig.5. Example two-channel displacement history for interpolation.

Once the map and history are specified, interpolation can begin. Endurica EIETM supports multi-threading, meaning that interpolation calculations can be distributed and executed in parallel across available CPUs. This makes interpolating very fast and very scalable to large models and lengthy histories. Note that Endurica EIETM generates large files because it calculates stress and strain tensor components for each time step of each finite element. It is therefore important to ensure that you have sufficient disk space available when running Endurica EIETM.

Comparing linear and non-linear interpolation results for a sway bar under uniaxial loading

As a first example, consider an automotive sway bar link, shown in Fig.7. The sway bar transmits load in a single axial direction. This model uses Ogden’s hyper elastic law, which involves a non-linear relationship between stress and strain. The large deformation solution also involves non-linear kinematics due to the incompressibility of rubber and finite displacements and rotations. To compare the linear and non-linear interpolation methods, we will run the analysis using both: 1) the linear scaling method (where the map consists of a single load case in which we apply one newton of total load in the x-direction to the link and solve for the strain distribution in the part); and 2) the non-linear method (where the map consists of 11 precomputed steps ranging from -10000N to +10000N).

Endurica sway bar analysis area noted by red arrows
Fig.6. Sway bar link under uniaxial loading (left). Axial load history input for strain history interpolation (right).

Figs. 8–10 show the six engineering strain tensor component history results for both the linear superposition procedure (left) and the nonlinear EIE procedure (right). The results are shown for three different locations on the sway bar bushing (highlighted in red). The largest strain component is the 31 shear (orange line). Note that for the linear procedure, a linear increase in the amplitude of the global force results in a linear increase in the strain components. The non-linear procedure produces quite different results. In fact, where the linear solution predicts symmetry of tension and compression loads, the non-linear solution correctly captures asymmetries.

Endurica Sway Bar Analysis linear and nonlinear
Fig.7. Comparison of linear (left) and non-linear (middle) interpolation results for strain tensor components at the location indicated on the right.
Enduria sway bar analysis top area
Fig.8. Comparison of linear (left) and non-linear (middle) interpolation results for strain tensor components at the location indicated on the right.
Endurica sway bar analysis top at edge
Fig.9. Comparison of linear (left) and non-linear (middle) interpolation results for strain tensor components at the location indicated on the right.

As a final comparison, Fig.11 shows the fatigue life calculated using Endurica CLTM. A longer fatigue life is predicted for the non-linearly interpolated case compared to the linearly interpolated case. Note that the fatigue damage is more concentrated in the linear case and more spatially distributed for the non-linear solution.

Endurica sway bar analysis Linear versus Nonlinear
Fig.10. Comparison of fatigue life calculations based on linear (left) and non-linear (right) interpolated strain history.

Endurica EIETMvalidation for a six-channel non-linear interpolation

As a further test of the non-linear interpolation procedure for a six-channel ( forces +  moments) multiaxial load analysis of the gearbox mount shown in Fig.11, the map shown in Fig.12 was defined. This map contained 51 precalculated non-linear FE solutions. The complete loading history to be interpolated is shown in Fig.13. This history was solved in full directly and interpolated from the map using Endurica EIETM.

Endurica Gearbox Mount Analysis
Fig.11. Gearbox mount analysis. All forces and moments (x, y, and z) were applied at the centre of the top rigid mounting plate.
Endurica Six-channel map containing 51 precalculated finite element solutions.
Fig.12. Six-channel map containing 51 precalculated finite element solutions.
Endurica Full six-channel road load history used for validation analysis of gearbox mount.
Fig.13. Full six-channel road load history used for validation analysis of gearbox mount.

The strain tensor histories for the 11, 22 and 12 strain components are compared between the directly solved and interpolated solutions in Fig.14 at the location of the most critical element. A fairly accurate interpolation was obtained with a much shorter run time than the direct finite element analysis of the full history.

Endurica Comparison of EIE-interpolated strain components (blue) v. direct finite element solution (red) at the location of the most critical element.
Fig.14. Comparison of EIE-interpolated strain components (blue) v. direct finite element solution (red) at the location of the most critical element.

The fatigue life of the gearbox mount was calculated with Endurica CLTM using both the EIE-interpolated strain history and the directly solved strain history. The fatigue contours for both cases are shown in Fig.15. The fatigue life for the interpolated history was 7.52E8 and for the directly solve history the fatigue life was 7.87E8. These results indicate a close agreement between the EIE and directly solved cases. Other validation cases were recently published elsewhere (Mars et al 2024).

Endurica comparison of fatigue life calculated from EIE-interpolated strain components (right) and direct finite element solution (left).
Fig.15. Comparison of fatigue life calculated from EIE-interpolated strain components (right) and direct finite element solution (left).

Conclusion

Analysis of rubber components typically involves strong nonlinearities due to material behaviour, finite strain kinematics, and contact. The traditional linear superposition of unit load cases, widely used in metal fatigue analysis, is not effective in such cases. Fortunately, the Endurica EIETM solver can generate strain histories efficiently and accurately in these cases. The EIE tools allow the analysis to precalculate a set of FE solutions for efficient discretization of the load space and accurate interpolation of signals within the load space. With sufficient discretization of the load space, it was shown that quite accurate results can be produced for cases where there are between one and six load input channels.

MORE

This article by Dr. Mars was published in Futurities magazine in Volume 21 No.3 Autumn 2024 issue on pages 34-38 which can be accessed by clicking here. Futurities is published by EnginSoft, a leading technology transfer company, and an Endurica reseller in Italy.

Dr. Mars originally presented this information in Endurica’s Winning on Durability webinar series. To view the webinar click here.

References

[1.] R. W. Landgraf, “Applications of fatigue analyses: transportation”, Fatigue ’87, vol. 3, pp. 1593–1610, 1987

[2.] Moon, Seong-In et al, “Fatigue life evaluation of mechanical components using vibration fatigue analysis technique”, Journal of Mechanical Science and Technology, vol. 25, pp. 631–637, 2011.

[3.] F. A. Conle and C. W. Mousseau, “Using vehicle dynamics simulations and finite-element results to generate fatigue life contours for chassis components”, International Journal of Fatigue, vol. 13(3), pp. 195–205, 1991.

[4.] K. P. Barbash and W. V. Mars, “Critical plane analysis of rubber bushing durability under road loads”, SAE Technical Paper No. 2016-01-0393, 2016.

[5.] W. V. Mars, “Interpolation engine for analysis of time-varying load data signals”. U.S. Patent 9, 645, 041, May 9, 2017.

[6.] W. Mars,  K. Barbash et al, “Durability of Elastomeric Bushings Computed from Track-Recorded Multi-Channel Road Load Input”, SAE Technical Paper No. 2024-01-2253, 2024.

 

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Combine Multiple Load Cases into a Block Cycle Schedule that Executes as a Single Endurica Job

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Our most recent Users Survey garnered two surprising requests:

  • “Very interested in ability to run a single model with increasing load and combine with “Duty cycle” definition to predict/calculate expected lifetime.”
  • “Would like to see more on how to use duty cycles (loads) within one analysis rather than running at one load.”

Endurica already does this! Allow me to break down the process and show how easy it is.

Multiple loading cases for a specific duty cycle is often part of Fatigue analysis. You can piece together a schedule of varying Loads, Displacements, Temperatures, Ozone Exposure, and more with Endurica DT.

I focus on load variability in this example. This duty cycle contains three unique loading conditions for a Simple Tension Strip: (A) 10mm displacement, (B) 20mm displacement, and (C) 35mm displacement.

Each load case is a separate FEA simulation. The strains are all exported separately for use with Endurica DT. Each FEA job is a single cycle of the desired loading.

Figure 1.  Contours of maximum principal engineering strain for each of load cases A, B and C. 

Here is a breakdown of the Duty Cycle for this analysis. One Cycle or “Life” is equivalent to 300 repeats of 10mm, 200 repeats of 20mm, and 100 repeats of 35mm.

Figure 2.  Block cycle schedule consisting of 300 repeats of load case A (displaced of 10mm), followed by 200 repeats of load case B (displaced of 20mm), and by 100 repeats of load case C (displaced of 30mm). 

When setting up the Endurica input file we specify the “schedule” under the “history” header in the input file. The number of “block_repeats” is then specified for each of the loading conditions. Once they are specified you submit the Endurica DT job like you would a single load Endurica CL job. The resulting life you receive will be the total number of cycles till failure.

Figure 3.  Endurica input file json syntax defining the block cycle schedule. 

Once submitted, Endurica provides a minimum life prediction of 2,944 Cycles of the full schedule. That is 883,200 cycles of 10mm, 588,800 cycles of 20mm, and 103,040 cycles of 35mm.

Figure 4.  Contours of fatigue life, reported as repeats of the total block cycle schedule. 

Want more information? Check out more details of Endurica DT’s capabilities.

For tutorials visit Endurica Academy:

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Rubber Fatigue ≠ Metal Fatigue Part 1: Mean Strain Effects

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Rubber Fatigue does not equal Metal Fatigue Part 1 Mean Strain Effects
Figure 1. Constant amplitude cycles at three different mean strains.

Rubber and metal are very different materials that exhibit very different behaviors.  Consider the effect of mean strain or stress on the fatigue performance of these materials.  Figure 1 illustrates a few typical constant amplitude strain cycles, each at a different level of mean strain.  If the stress amplitude is equal to the mean stress, we say that we have pulsating tension or fully relaxing tension.  If the mean stress is zero, we say that we have fully reversed tension/compression.  If the minimum stress is always positive, then we have nonrelaxing tension (i.e. always under load).  Nonrelaxing cycles are quite common in applications.  Examples include: pre-loads applied during installation; swaging of a bushing to induce compressive pre-stresses, interference fits, self-stresses occurring due to thermal expansion/contraction; and in tires, shape-memory effects of textile cords.

In metal fatigue analysis, it is customary to define the effect in terms of stress amplitude σa and mean stress σm, relative to the yield stress σy and the ultimate stress σu, as shown in Figure 2.  Below the fatigue threshold stress σ0, indefinite life is predicted. The Haigh (or Goodman)

Figure 2. Haigh diagram (left) and Wohler curves (right) showing mean strain effects on fatigue life for a metal.

diagram (left) maps fatigue life as a function of these parameters [1]. Wohler curves (right) provide similar information.  For metals, a simple rule may be applied universally: increasing mean strain is detrimental fatigue life.  It is also commonly assumed for metals that the critical plane is perpendicular to maximum principal stress direction.

There are many ways that rubber materials differ from metallic materials.  At the atomic scale, rubber is composed of long chain molecules experiencing constant thermal motion while interlinked with a permanent network topology.  This structure permits large, elastic/reversible straining to occur.  Metals could not be more different, existing as individual atoms packed into well-ordered crystals with occasional dislocations or lattice vacancies.  This structure permits only vanishingly small strains before inelastic deformation occurs.  At the meso scale, rubber is typically a composite material containing fillers such as carbon black, silica or clay, as well as other chemical agents.  The mesoscale of a metal is generally described in terms of crystalline grain boundaries and inclusions or voids.  Rubber exhibits many “special effects” that are not seen in metals: rate and temperature dependence, ageing, cyclic softening.  It is unsurprising that analysis methods for rubber differ substantially from those applied for metals.

Rubber’s fatigue performance has a more complex dependence on mean strain. For amorphous (ie non-crystallizing) rubbers, increasing mean strain reduces the fatigue life, as with metals.  But for rubbers that exhibit strain-induced crystallization, mean strain can greatly increase fatigue life, as illustrated in Figure 3.  Fatigue simulations therefore must take account of the strain crystallization effect.

Figure 3. Fatigue tests run in simple tension under constant amplitude show a significant increase in life for Natural Rubber (NR), which strain crystallizes, and a decrease of life for Styrene Butadiene Rubber (SBR) which is amorphous [2].
Mean strain effects are specified in the Endurica fatigue code in terms of fracture mechanical behavior, using the concept of an equivalent fully relaxing tearing energy Teq.  The tearing energy for fully relaxing conditions is said to be equivalent when it produces the same rate of crack growth as the nonrelaxing condition.  For amorphous rubbers, the equivalent R=0 tearing energy Teq is simply the range ΔT of the tearing energy cycle, which can be expressed in terms of the min and max tearing energies Tmin and Tmax, or in terms of R= Tmin / Tmax.  Plugging this rule into the power law crack growth rate function yields the well known Paris law, which predicts faster crack growth for increasing mean strain.  For a strain crystallizing rubber, the equivalent fully relaxing tearing energy can be specified using the Mars-Fatemi law.  In this case, the equivalent fully relaxing tearing energy depends on a function F(R), which specifies the crystallization effect in terms of its influence on the powerlaw slope of the crack growth rate law.  The relationship for amorphous and crystallizing rubbers are summarized in Table 1 [3,4].

Table 1.  Models for computing crack growth rate in amorphous and strain-crystallizing rubbers.

Rubber’s fatigue behavior may be plotted in a Haigh diagram, but the contours can be quite different than for metals.  In metal fatigue analysis, it is assumed that cracks always develop perpendicular to the max principal stress direction. This is not always true for rubber, especially in cases involving strain crystallization and nonrelaxing loads.  For rubber fatigue analysis it is therefore required to use critical plane analysis [5], in which fatigue life is computed for many potential crack orientations, and in which the crack plane with the shortest life is identified as the most critical plane.  Figure 4 shows the dependence of the fatigue life and the critical plane orientation on strain amplitude and mean strain.  A sphere is plotted for each pair of strain amplitude and mean strain coordinates, on which the colors represent fatigue life, and unit normal vectors indicate critical plane orientations.  It can be seen that different combinations of mean strain and strain amplitude can produce a range of crack plane orientations.

Figure 4. Critical plane analysis consists in integrating the crack growth rate law for every possible crack orientation, and identifying the orientation that produces the shortest life (left). Each point in the Haigh diagram (right) is associated with its own critical plane orientation.

The Haigh diagrams for natural rubber (NR) and for styrene butadiene rubber (SBR) are shown in Figure 5.  In these images, red represents short fatigue life, and blue long life.  For natural rubber (on the left), the long-life region of the Haigh diagram exhibits a notable dome-like shape, indicative of a beneficial effect of mean strain under the influence of strain-induced crystallization. In contrast, SBR always exhibits decreased fatigue life as mean strain increases.  Even so, the Haigh diagram for SBR has a nonlinear character associated with the material’s hyperelasticity that is also distinct from a metal.

Figure 5. Haigh diagrams computed for NR (left) and for SBR (right) rubbers.

It should be noted that the strain crystallization effect in rubber depends on temperature.  At colder temperatures, the effect is stronger, and at higher temperatures it is weaker.  Figure 6 compares experimental Haigh diagrams [6] (top) for a crystallizing rubber to computed results (bottom) for three temperatures.

Figure 6. Experimental Haigh diagram [6] for natural rubber at 3 temperatures (top), compared to computed Haigh diagram (bottom). Increasing temperature tends to reduce the beneficial effect of strain crystallization.
In summary, while tensile mean stresses are always detrimental in metals, in rubber they may be either beneficial or harmful, depending on whether the rubber can strain crystallize. The benefits of mean stresses in rubber can be quite strong – sometimes amounting to more than several orders of magnitude. The beneficial effect is stronger at colder temperatures and is reduced at higher temperatures.  Critical Plane Analysis is essential for accurately predicting the effects of strain crystallization in rubber.  Wohler curves, commonly used for metal fatigue analysis, incorrectly assume that the worst-case plane is always normal to the max principal stress direction.  This is not an accurate approach for strain crystallizing rubber under mean strain.  Use the Endurica fatigue solvers to accurately capture these effects when its important to get durability right!

MORE

This article by Dr. Mars was published in Futurities magazine in Volume 21 No.2 Summer 2024 issue on pages 36-38 which can be accessed by clicking here. Futurities is published by EnginSoft, a leading technology transfer company, and an Endurica reseller in Italy.

Dr. Mars originally presented this information in Endurica’s Winning on Durability webinar series. To view the webinar click here.

References

[1] Stephens, R. I., Fatemi, A., Stephens, R. R., & Fuchs, H. O. (2000). Metal fatigue in engineering. John Wiley & Sons.

[2] Ramachandran, Anantharaman, Ross P. Wietharn, Sunil I. Mathew, W. V. Mars, and M. A. Bauman.  (2017) “Critical plane selection under nonrelaxing simple tension with strain crystallization.” In Fall 192nd technical meeting of the ACS Rubber Division, pp. 10-12.

[3] Mars, W. V. (2009). Computed dependence of rubber’s fatigue behavior on strain crystallization. Rubber Chemistry and Technology, 82(1), 51-61.

[4] Harbour, Ryan J., Ali Fatemi, and Will V. Mars. “Fatigue crack growth of filled rubber under constant and variable amplitude loading conditions.” Fatigue & Fracture of Engineering Materials & Structures 30, no. 7 (2007): 640-652.

[5] Mars, W. V. (2021). Critical Plane Analysis of Rubber. Fatigue Crack Growth in Rubber Materials: Experiments and Modelling, 85-107.

[6] Ruellan, Benoît, J-B. Le Cam, I. Jeanneau, F. Canévet, F. Mortier, and Eric Robin. “Fatigue of natural rubber under different temperatures.” International Journal of Fatigue 124 (2019): 544-557.

 

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Tolerances in Fatigue Life Prediction with Endurica

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I get this question a lot: how well can the Endurica software predict fatigue life?  Is it as good as a metal fatigue code, where a factor of 2x is often quoted as a target tolerance?

The answer is yes, fatigue life predictions can reach and beat this level of accuracy. But as always, knowledge and control of the problem at hand is key.  We must keep in mind that fatigue behavior varies on a logarithmic scale.  It depends on many variables.  It depends on how failure is defined in the simulation and in the test.  Small variations of an input may lead to large variations of the fatigue life.  So, to achieve the best tolerances, careful specification, measurement, and control are required of both simulation and test.

Analysis tolerances depend on whether the analysis workflow is “open loop” or “closed loop”.  In an open loop workflow, the analyst is typically in the position of having to accept without question the as-given material properties, geometry, boundary conditions and load history.  The analysis is completed and reported.  Decisions are made and life goes on.  In a closed loop workflow, there are additional steps.  These include a careful review of differences between the test and the simulation, as well as identification and correction of any erroneous assumptions (about material properties, geometry, boundary conditions, and load history).

Open loop workflows produce larger tolerances.  Every situation is different, but do not expect tolerances tighter than perhaps a factor of 3x-10x in life, when working in open loop mode.  There is just too much sensitivity, too many variables, and too little control in this mode.  The open loop mode does have a few advantages though.  It takes less work, less time, less cost.  And it is often useful for ranking alternatives (ie A vs. B comparisons).

For high accuracy, a closed loop workflow is required.  It is rarely the case that initial assumptions are sufficiently error-free to support tight tolerances on fatigue life prediction.  Therefore, careful measurement and validation of material property inputs, part dimensions, load-deflection behavior, pre-stresses, etc. should be made.  Where gaps are found between test and simulation, appropriate amendments to the test and/or to the simulation should be adopted.  This approach yields high confidence in the simulation results, and good accuracy in fatigue life predictions.  We have seen users hit life predictions to better than a factor of 1.1x with this approach!  Although this approach requires more effort, it results in more complete mastery of part design, and it yields a much stronger starting position for subsequent products.

While “right the first time” engineering is possible with either open or closed loop, the closed loop approach benefits from progressive refinement of the analysis inputs and it ultimately gives the highest success rate.

 

 

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What is the Price of Standing Still?

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What if we don't change at all and something magical just happens? Technical equation for entropy

“We have always done it this way.” No longer simply a hated phrase, this statement is a warning of impending disaster. Entropy – the disorder that happens when energy disperses and systems simply fall into chaos – happens when things do not change. But it’s a slow process you don’t see day-to-day. Continuing with traditional “build and break” development methods instead of embracing CAE and simulation has many long-term risks but it will only be after stagnating for some time that rubber parts manufacturing firms, and even the entire rubber industry, will realize the pitfalls:

Talent Loss
People are the key to it all and we start here since intelligent, hard-working, productive people are the fundamental reason any business succeeds. When the best and brightest employees leave a company, the fundamental reasons often include the lack of opportunity, learning, and career development. When not allowed to work with emerging technologies and are no longer challenged to grow, top performers find new opportunities taking not only raw potential but also institutional memory with them. And if they don’t see the industry as a viable long-term option, switching companies can also mean leaving the sector completely.

Warranty Issues/Payouts
Liability issues arise when product usage, applications and environments bring risks that may not have been factored in to the original designs and/or production methods. Traditional testing methods cannot be used to investigate “what if?” scenarios the way CAE and simulation can. Recalls and litigation can be significantly more costly than new technology implementations.

Lost Opportunity Costs
While harder to measure than fixed and variable business costs, there is an expense to every choice known as opportunity cost. Refusing to enter a new business sector may result in significant loss of revenue and profit. Taking on a big client project may strain production capabilities. “Standing still” eliminates those risks, but at what potential gain? As the rubber industry wrestles to “go green” we are all weighing and measuring the opportunity costs involved. The real lost opportunity is in refusing to embrace a fundamentally better design platform.

Incompatibility or Obsolescence
At some point, everything being produced right now will become obsolete. Even if you produce the best “widgets” anywhere, the environment around that “widget” will change and will no longer be needed in its current form. The rubber industry standard procedure of building a product then breaking it in physical testing to determine the next design rendition is incompatible with the time available for new product development. It just does not work anymore.

How quickly your business can adapt to or anticipate change is a key factor in continued success. The reasons companies do not make continued progress often include:

Change is expensive
Investments in training, new production systems, updated software and computers add up, but these numbers are not insurmountable when factored against the ongoing and often increasing costs of waste, repairs and downtime associated with outdated systems and equipment.

Learning new technology is time-consuming
Remember when you were thinking about going to college and four (6-8-10) years seemed like FOREVER? What was your ROI? What will it be now? Time invested in learning reaps many rewards beyond the subject at hand and often provides renewed overall energy.

The status quo works
For today, yes. For a brighter future for you company and the industry, NO. Companies that don’t evolve face certain death. Day-to-day operations may appear stable, but firms who do not keep up with technology do not stay in business. Covid forced many to embrace technology in new ways and those firms continuing to provide progressive working arrangements are gathering more than their fair share of the best and brightest talent. Enabling people to work beyond traditional geographic boundaries requires accountability and processes for measuring valued contributions rather than simply time at a desk.  Firms embracing CAE and simulation technologies have realized this and are at the top of the leading rubber industry rankings.

 Six reasons to adopt Endurica workflows

  1. Technically superior (click for details)
  2. Save big on development out of pocket costs (click for details)
  3. Reduce the need for physical testing (see page 2, blue box on right)
  4. Speed to market (able to use the tools immediately)
  5. Accuracy in meeting client needs (click for details)
  6. Easier answers down the road (click for details)
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My SAE WCX 2022 Top Takeaway

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SAE WCX | Detroit, Michigan | April 5-7, 2022

There were several papers on fatigue life prediction for elastomers at SAE WCX 2022, but the highlight for us was this one from Automotive OEM Stellantis: “Fatigue Life Prediction and Correlation for Powertrain Torque Strut Mount Elastomeric Bushing Application” by Dr. Touhid Zarrin-Ghalami, Durability Technical Specialist at FCA US LLC Fiat Chrysler Automobiles logowith coauthors C Elango, Sathish Kumar Pandi, and Roshan N. Mahadule from FCA Engineering India Pvt, Ltd.  Check out the abstract or buy the paper here…

The study shows that very accurate fatigue life prediction results are possible for elastomeric components under block cycle loading using Critical Plane Analysis.  A key feature of the analysis is the characterization and modeling of rubber’s hyperelastic properties, fatigue crack growth properties, crack precursor size, and strain crystallization behavior.  Careful measurement of these analysis ingredients led to a nearly perfect correlation of the predicted life (520 blocks) with the tested life (523 blocks, average of 4 replicate tests), and of predicted failure mode with observed failure mode.

Endurica users like Stellantis are developing a solid track record of routine and successful fatigue life prediction.  We soon expect to see the day when CAE fatigue life prediction for rubber components is regarded as obligatory, given the risk and cost avoided with “right the first time” engineering.

Congratulations to the Stellantis team on this impressive success!

Fatigue Life (block) demonstrating the accuracy of the CAE Virtual Simulation compared to a physical test

Citation: Elango, C., Pandi, S.K., Mahadule, R.N., and Zarrin-Ghalami, T., “Fatigue Life Prediction and Correlation of Engine Mount Elastomeric Bushing using A Crack Growth Approach,” SAE Technical Paper 2022-01-0760, 2022, doi:10.4271/2022-01-0760.

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Virtual vs. Physical in 2021 and Beyond

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An insight to how Endurica stayed connected during Covid-19, by using Microsoft teams to meet virtually.These days everybody’s talking about whether to meet in person or online.  There are great tools available for online meetings, and these have helped us navigate Covid-19. Like everyone else, Endurica teammates regularly use online meeting technology.  But if there is one thing we learned over the last year, it is that sometimes physical presence really matters. Living and working in isolation is just not healthy in the long run.

The new normal during the pandemic had some benefits that were enabled by the virtual world. Time and energy that used to be consumed by travel were rechanneled into improving our software, testing services, and marketing materials. In our personal lives, we had more opportunities to spend quality time with our immediate families and found more time for fitness activities. We previously talked about our pandemic pivots to bring our training courses online and offer webinars to stay in touch with our existing and potential customers.

But virtual meetings can’t replace the full experience of being together in person.  The face-to-face engagement at a trade show, the serendipitous bumping into a client, the spontaneous discussion of ideas with fellow conference-goers with a shared interest, the rapport building that comes from shared experiences.  We fundamentally need physical connection. A hug, delivered via Zoom, will never feel the same.

The world of 2021 and beyond is hybrid: part virtual, part in-person.  The benefits of the virtual are too great to set aside, and the necessity of the physical is too compelling to neglect.  Both are critical to our future, at home and at work.

So, too, with Endurica’s simulation workflows. It was NEVER Simulation OR Build-and-Break. Even the best simulations are not enough to completely skip physical testing. The virtual approach saves significant time and money in product development and design refinement. It allows you to explore a huge space of compound options and of design features before investment in building and testing prototypes. Our simulations enable you to balance difficult trade-offs. Still, before you head into production, you must complete actual physical testing on your rubber part – the physical world is what counts in the end. It is simulation AND build-and-break that are both needed in concert to #GetDurabilityRight.

Just as a Zoom hug will never replace the real thing, software will never replace the role of physical testing.  But just as online meetings are creating new opportunities and efficiencies, Endurica’s tools position you for unprecedented success when it’s time to test.

It's a Hybrid World from Here | Endurica's tools position you for unprecedented success when it’s time to test.

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Proper tear testing of elastomers: Why you should tear up the Die C tear test

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Endurica Fatigue Ninja tearing rubber

I spent an interesting and rewarding part of my career helping to lead an elastomer technical college in Yanbu, Saudi Arabia. One of the rubber technology words that was challenging for the Saudis to say in English was ‘tear’. They initially pronounced it like the heteronym related to crying. It might be a stretch to say that tears will come to your eyes if you don’t get tear testing of elastomers right, but proper measurement of critical tearing energy (tear strength) is essential for effective materials development for durability.

The fatigue threshold (intrinsic strength; T0) is the lower limit of the fatigue crack growth curve shown in the figure below, and we recently reviewed this material parameter including the various measurement options.1 The upper limit is the tear strength, TC. If loads in your elastomer component are near or above TC, then it is not a fatigue problem anymore but rather a critical tearing issue with imminent product failure. It is therefore important to accurately characterize this durability performance characteristic of your materials.

General fatigue crack growth behavior of elastomers

Endurica uses the planar tension (pure shear) geometry for measuring TC in our Fatigue Property Mapping testing services due to the simple relationship between the strain energy density (W) and the energy release rate (tearing energy, T).2,3 The TC is equal to the W at tearing multiplied by the initial specimen height, h. You can see this geometry below along with other tear testing specimens employed in the rubber industry and specified in the ASTM standard.4

Comparison of the different durability tests one can conduct: the differences between Crack Nucleation Test and Tear and Crack Growth Tests.

We sometimes get questions from folks with technical backgrounds in metals or plastics about whether rubber tear properties will be different when tested in distinct testing modes (mode I, mode II, etc.). It turns out that the extensibility of rubber causes the deformation to be predominately tension in the tearing region, irrespective of how the crack is opened, such that TC values are similar for rubber evaluated in different testing modes.2,3 Therefore, trouser tear testing is an alternative to the planar tension testing, as long as any stretching of the legs is accounted for in the data analysis.3,5 With no stretching of the legs, TC is simply given by 2F/t where F is the measured force to propagate the tear and t is the thickness of the specimen. The factor of 2 is surprisingly omitted in the ASTM standard4 even though it is mentioned in the appendix. The image below shows how to convert the ASTM trouser tear strength to TC.

Trouser tear strength testing

A proper tear test includes an initial macroscopic cut/crack in the specimen. This is not the case for Die C tear described in the tear testing standard.4 Die C is thus not a tear test at all but rather is a crack nucleation experiment akin to normal tensile testing of rubber. Because the strange Die C geometry forces failure in a small region in the center of the specimen, it is actually less useful than tensile strength testing of a dumbbell sample which probes the entire gauge region. The Die C test can also have substantial experimental variability related to the sharpness of the die used to punch out the samples. Unfortunately, the Die C “tear” test is the most popular method in the rubber industry to (incorrectly) assess the tear strength of elastomers, and this reality was a key motivator for writing this post. We look forward to seeing the rubber industry shift away from the Die C test, and we hope that the information provided here will help in that path to #GetDurabilityRight. Click here to learn how intrinsic strength and tear strength can be measured quickly and accurately (0:42 video).

References

  1. Robertson, C.G.; Stoček, R.; Mars, W.V. The Fatigue Threshold of Rubber and its Characterization Using the Cutting Method. Advances in Polymer Science, Springer, Berlin, Heidelberg, 2020, pp. 1-27.
  2. Lake, G.J. Fatigue and Fracture of Elastomers. Rubber Chem. Technol. 1995, 68, 435-460.
  3. Rivlin, R.S.; Thomas, A.G. Rupture of rubber. I. Characteristic energy for tearing. J. Polym. Sci. 1953, 10, 291–318.
  4. Standard Test Method for Tear Strength of Conventional Vulcanized Rubber and Thermoplastic Elastomers. Designation: ASTM D 624-00, ASTM International, West Conshohocken, PA, USA, 2020; pp. 1-9.
  5. Mars, W.V.; Fatemi, A. A literature survey on fatigue analysis approaches for rubber. Int. J. Fatigue 2002, 24, 949–961.
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