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Fatigue Life Prediction of an Automobile Cradle Mount

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Copyright © 2013 SAE International

ABSTRACT

Elastomers have large reversible elastic deformation, good

damping and high energy absorption capabilities. Due to these

characteristics along with low cost of manufacturing,

elastomeric components are widely used in many industries

and applications, including in automobiles. These components

are typically subjected to complex multiaxial and variable

amplitude cyclic loads during their service life. Therefore,

fatigue failure and life prediction are important issues in the

design and analyses of these components. Availability of an

effective CAE technique to evaluate fatigue damage and to

predict fatigue life under complex loading conditions is a

valuable tool for such analysis. This paper discusses a general

CAE analytical technique for durability analysis and life

prediction of elastomeric components. The methodology is

then illustrated and verified by using experimental fatigue test

results from an automobile cradle mount. The developed

methodology involves constitutive behavior and fatigue

behavior of the material, finite element analysis of the

component, and fatigue damage quantification for life

predictions. The commonly used Rainflow cycle counting

method and Miner linear cumulative damage rule for metals

are also evaluated for their application to variable amplitude

loading of elastomeric components. The experiments included

axial as well as combined in-phase and out-of-phase axial-

torsion constant amplitude and variable amplitude tests.

Comparisons of the predictions with experimental results

show that the developed methodology correctly predicts the

failure location. It also provides reasonably accurate estimates

of the fatigue initiation life.

INTRODUCTION

Elastomeric components have a wide usage in many

applications especially at automotive industry and their field

of application has broadened in recent years. Car tires, bumper

components, engine mounts and cradle mounts are some of the

examples. Rubber mounts are typically used as vibration

isolators in vehicles. Their function is damping

high-amplitude and low frequency road induced vibrations in

cradle mounts and low-amplitude high frequency engine

induced vibrations in engine mounts. Most of these

components typically operate under repeated loads over a

period of time which makes them prone to fatigue failure.

Therefore, it is necessary to deal with durability and fatigue

failure aspects of elastomeric components and fatigue life

evaluation is an important consideration in their design to

assure their safety and reliability.

Several inputs are necessary for fatigue life prediction of

elastomeric components. These are relevant material

properties, loading history and the component geometry. For

fatigue analysis, first stress and/or strain history at critical

location(s) of the component could be obtained via finite

element analysis. Then, using the obtained history, a proper

fatigue damage quantification parameter and a cumulative

damage rule are needed to predict the fatigue life.

The elastomer’s material behavior is complex due to high

deformability, quasi incompressibility, stress softening, and

time-dependent effects. Therefore, a reliable analysis must

include these characteristics. Also, properties of rubber can

change drastically depending on material composition,

manufacturing conditions, loading condition and

environmental conditions. Mars and Fatemi discussed the

aforementioned effects in detail in [1].

Mars and Fatemi [2] performed a literature survey on different

approaches of fatigue analysis for rubber. They classified

fatigue failure process is into two distinct phases, crack

initiation phase in which crack nucleates in part of the material

that was initially crack free, and crack growth phase in which

the initiated cracks grow to failure or rupture. They mentioned

that maximum principal strain and strain energy density are

two broadly used fatigue damage quantification parameters for

the crack initiation stage.

Li et al. [3] performed fatigue life prediction of a rubber

mount by using the maximum principal strain at the critical

region obtained from FEA as a fatigue damage parameter. To

verify their analysis, they conducted constant amplitude

load-controlled fatigue experiments in directions

perpendicular to the mount axial direction. Their results

showed good agreement with the predicted fatigue lives.

Page 2 of 10

Kim et al. [4] used the maximum Green-Lagrange strain and

the maximum energy density as fatigue damage parameters for

life predictions in another study on an engine rubber mount.

They obtained material fatigue-life equations from fatigue

experiments of dumbbell-shaped specimens. Then by utilizing

FEA, a load versus Green-Lagrange strain relation was

determined. They concluded that the Green-Lagrange strain is

a better fatigue damage parameter than the strain energy

density for component life predictions based on their load-

controlled constant amplitude fatigue tests of rubber engine

mount.

Woo et al. [5] studied the fatigue life of natural rubber

components and used the Green-Lagrange strain at a critical

location for damage evaluation. To validate their analysis,

displacement-controlled fatigue tests with different values of

mean displacement and amplitude were conducted. Their

experimental results showed reasonable results compared to

the predictions.

Luo and Wu [6] conducted fatigue failure analyses of rubber

springs, which are widely used as anti-vibration components.

Their study showed the capability of nonlinear

quasi-static FE simulation for modeling geometric and

material nonlinearities of elastomeric components in product

design and failure analysis. They analyzed fatigue life of

anti-vibration rubber springs used in a rail vehicle suspension

system [7-9]. Mooney-Rivlin hyper-elastic material model and

FEA were used in their study to obtain the stress contour. By

using the S-N curve obtained from uniaxial loading, they

performed fatigue life predictions and proposed a three-

dimensional effective stress criterion describing an ellipsoidal

failure envelope for fatigue failure based on principal stress

values. They conducted fatigue tests on two types of rubber

springs in the longitudinal direction under uniaxial loading

and their experimental results indicated good agreement with

the predictions for both crack initiation location and direction

[9].

Zhao et al. [10] studied a rubber mount using a FEA method.

They found that the main reason for fatigue cracking was the

stress concentration at the interfaces between the rubber and

metal layers. This was also observed in their constant

amplitude mount fatigue testing. They then modified the

geometry of the mount and changed the shape of the inner

bushing by dig grooving in the rubber layers which resulted in

a reduction of maximum equivalent strain due to lower stress

concentration and, therefore, improved fatigue life.

Kim et al. [11] performed a study on fatigue life prediction of

automotive rubber components under variable amplitude

loading. They conducted fatigue testing in displacement

control and used the maximum Green-Lagrange strain as a

damage parameter for analysis. The SAE transmission load

history [12] was used in their study. The relationship between

displacement and fatigue life was generated by fatigue testing

of dumbbell specimens in displacement control. By utilizing

the Odgen strain energy density function and FEA, they

related the maximum Green-Lagrange strain at the critical

component location to displacement, and subsequently to

fatigue life. The complex load history was simplified by using

the racetrack cycle counting method. Their results which were

obtained based on Miner’s linear damage rule indicated fairly

good agreement, with a factor of two correlation between the

predicted and the experimental fatigue lives.

Andre et al. [13] conducted torsion experiments on rubber

specimens with an axisymmetrical notched geometry. They

concluded that the maximum principal Cauchy stress is related

to multiaxial fatigue damage mechanisms and proposed that

this parameter could be used as a fatigue damage

quantification parameter. They also observed that the crack

orientation was perpendicular to the maximum principal stress

direction.

A crack initiation approach which is used in this current study

is normally related to the macroscopic continuum mechanics

quantities such as stress or strain. The maximum principal

Green-Lagrange strain, the maximum principal Cauchy stress,

and the strain energy density (SED) are some examples of the

parameters which are typically used for this approach. Critical

plane approaches such as the cracking energy density (CED)

or the approaches based on configurational mechanics such as

Eshelby stress tensor [such as in 15] are more complex and

recent approaches which are appropriate to deal with

multiaxial fatigue analysis of elastomers. However, the

maximum principal Green-Lagrange strain criterion

introduced by Cadwell et al. [13] still remains one of the most

widely used criteria. The commonly used parameter of strain

energy density (SED) has some drawbacks including inability

to differentiate between simple tension and compression,

therefore, inability to account for crack closure. SED criterion

cannot account for the fact that all of the stored energy in the

material would not release due to crack growth [16].

Mars and Fatemi [17] showed that scalar equivalence criteria

were not capable of predicting the fatigue initiation life in

natural rubber and suggested using the cracking energy

density (CED) which is the portion of the strain energy density

that is available to cause crack growth on a particular plane.

The application of this method needs knowledge of the

constitutive behavior of the material. In another study Harbour

et al. [18] used the maximum normal strain to find the critical

plane and then the cracking energy density on that plane as a

damage quantification parameter to determine fatigue life.

Their results showed similar fatigue life predictions compared

to cracking energy density. Because of the fact that maximum

normal strain is independent of constitutive behavior, the

critical plane can be identified easier than when using the

CED.

The main objectives of this study was using CAE durability

analytical techniques for predicting crack initiation life of an

automotive cradle mount and validate the results under

different constant and variable amplitude uniaxial and

multiaxial loadings. The capabilities of the rainflow cycle

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counting procedure and Miner’s linear damage rule are also

evaluated with component testing. A filled natural rubber

material with 21% carbon black and 9.5% plasticizer was used

in manufacturing of the cradle mount used.

In this paper, the cradle mount and FE modeling aspects are

first presented. Then the experimental work conducted on the

component is discussed. Finally, life predictions based on the

developed methodology involving cycle counting, cumulative

damage, and damage parameter is presented in terms of

correlations between the predicted and the experimental

results. This methodology relates the fatigue properties

obtained from material specimens under constant amplitude

fatigue tests to service loading conditions. An optimum

method for crack initiation life prediction is also described.

CRADLE MOUNT FINITE ELEMENT

MODELING

The rubber component evaluated was a cradle mount in a

vehicle. Component geometry is shown in Figure 1(a). The

nonlinear FE program ABAQUS was used to simulate the

nonlinear and large deformation behavior of the mount made

of hyper-elastic rubber material. The FE mesh is shown in

Figure 1(b) with a relatively fine mesh of about 30,000

elements to adequately model the geometry. Three-

dimensional eight node brick (hexahedral) elements with an

approximate size of 1 mm x 2 mm x 2 mm were used in this

model. Fully hybrid formulation elements with full integration

[19] were used for large deformations due to lower distortion

[20]. The output stress was from the integration point of the

element, therefore, an averaged quantity in the element.

The Marlow strain energy density form was used to

characterize deformation of incompressible isotropic

elastomers in the software. In order to simulate a load cycle

efficiently for fatigue loading, the “amplitude” tool of the FE

software was used. Stable deformation curve for the material

used in manufacturing the cradle mount was obtained by

incremental step tests conducted on a simple tension specimen

geometry. Significant softening was observed during initial

straining cycles due to Mullin’s effect. However, this behavior

was stabilized after about 20 cycles. The stable loops at

different strain levels are shown in Figure 2 [21]. These tests

were conducted at frequencies between 0.03 and 0.1 Hz,

depending on the applied stress range. Primary hyper-elastic

curve is constructed by fitting peak strain and peak stress

points of the different stabilized hysteresis loops [22], as

shown in Figure 2. Cyclic stable deformation curve was

applied as an input to the model, therefore initial softening

was inherently considered.

To model the hyper-elastic behavior of the rubber as a highly

non-linear elastic material with incompressibility, strain

energy potential is typically used. Strain energy potential

defines the strain energy stored at a point as a function of the

strain at that point assuming the material is isotropic and

homogeneous. In the case of Marlow form which was used in

this study, strain energy potential is constructed by direct

integration of deformation curve to reproduce the test data

exactly for a given deformation state. Therefore, the Marlow

model does not assume any explicit form [23]. This model has

reasonable behavior in other deformation states as well.

Drucker stability check was performed in the software for

judging the quality of fit to experimental data [19] to assure

the tangential material stiffness is positive definite.

(a)

(b)

Figure 1. (a)Vehicle cradle mount used and, (b) FE model

mesh.

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Figure 2. Stable cyclic stress-strain loops from incremental

step tests at different peak strain levels obtained from a

simple tension test [21].

For variable amplitude loading, the load history shown in

Figure 3 was used [24]. ABAQUS uses the same deformation

curve for loading and unloading. This corresponds with the

actual component behavior as observed from midlife

hysteresis loops [25]. Quasi-static implicit simulation type was

conducted for all of the loading conditions. Load and/or

displacement are applied to the reference point which is

coupled with inner FE nodes of the mount at the interface with

metallic part by utilizing the rigid body constraint capability of

the software, depending on the simulation type. To prevent

rigid body motion the outer portion of the mount was fixed.

More details of FE model can be found in [25]. Since the

critical element location is the site for crack initiation,

maximum principal strain and R ratio at the integration point

of this element (therefore, the averaged value in the element)

were obtained from FE simulation for each individual cycle or

block of loading.

The numerical results show that multiaxial states of stress and

strain are present at the critical location of the component.

Maximum principal strain distributions of the cradle mount

under uniaxial loading of R = 0.2 and load amplitude of

1,500 N is shown in Figure 4. The maximum principal strain

location was at the interface between the inner bushing and the

bulk rubber material at a location of abrupt geometry change.

This region is the critical region where fatigue cracks are

expected to nucleate. The stress and strain history obtained at

this point was used for evaluating the fatigue damage

parameter. This critical location was also observed to be the

site of fatigue cracking during the fatigue testing of the

component, which was the same for all of the simulations with

different load R ratios and load amplitudes.

(a)

cycle max min range mean % Damage

2-3-2' 16 -78 94 -31 2.39

4-5-4' 53 -79 132 -13 6.62

7-8-7' 6 -91 97 -43 2.61

9-10-9' 56 -91 147 -18 9.20

11-12-11' 45 -89 134 -22 6.96

14-15-14' 67 6 60 36 0.51

13-16-13' 75 -91 165 -8 13.04

18-19-18' 62 -50 112 6 4.10

22-23-22' 7 -53 60 -23 0.51

6-17-6' 93 -96 189 -2 19.52

20-24-20' 48 -95 143 -23 8.44

25-26-25' 33 -41 74 -4 1.14

27-28-27' 21 -40 61 -10 0.55

29-30-29' 17 -64 82 -23 1.53

1-31-1' 100 -99 199 0 22.71

32-33-32' 100 53 46 76 0.17

100.00

(b)

Figure 3. (a) Loading history used for random loading tests

of cradle mounts in load control, and (b) Rainflow cycle

count for max/min values of ±100 with relative damage

distribution from each cycle [24].

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Figure 4. Maximum principal strain distribution under

uniaxial loading of R =0.2 and load amplitude of 1,500N .

EXPERIMENTAL WORK

To validate the fatigue life prediction methodology, cradle

mount component deformation and fatigue tests were

conducted under different loading conditions and control

modes. Stiffness evaluation experiments were conducted as

well. Fatigue tests were performed with a sinusoidal waveform

for constant amplitude loadings by using a servo-hydraulic

axial-torsion load frame with load capacity of 50 kN.

Stiffness evaluation and comparison with

FE results

A monotonic compression test of the mount under

displacement control was conducted to compare with the FEA

simulation results. For FE simulation of this test condition

monotonic stress-strain curve [21] was used as the input. Also,

to account for initial softening, before the monotonic test 30

pre-cycles were applied at the intermediate displacement level.

Figure 5(a) shows stiffness comparison between the numerical

simulation and test results, indicating a difference of 14%.

The lower stiffness response from the test, compared to FEA

prediction, may be attributed to the 30 applied pre-cycles to

account for the initial softening.

Cyclic incremental step experiments at 1 Hz and 3 Hz with

R ~ 0 under displacement control were also conducted to

compare with the simulation results. In order to avoid transient

softening effect, 50 cycles at intermediate displacement levels

were applied prior to each displacement amplitude increment.

At each displacement level 260 cycles were applied and the

results from the last cycle are assumed to represent the

stabilized behavior for that test level. Finite element

simulations used the stabilized cyclic material behavior from

specimen simple tension tests, as well as the SED function of

Marlow, as discussed earlier and depicted in Figure 2. Figure

5(b) shows the comparison between the simulation and test

results. Based on this figure, the experimental cyclic curves

agree well with FEA predictions.

(a)

(b)

Figure 5. Stiffness comparison between FEA simulation and

(a) monotonic test of the mount and (b) cyclic tests of the

mount [25].

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Constant amplitude component uniaxial

fatigue tests

Constant amplitude uniaxial component fatigue tests were

conducted at ambient temperature under load-controlled

conditions with a sinusoidal waveform of 0.5 to 1 Hz.

Displacement amplitude response of each component was

periodically recorded. In order to define the fatigue crack

nucleation life of the cradle mount, cracking of several mounts

was also monitored by visual observation and direct

measurements throughout the test.

During initial cycles and because of Mullin’s effect, the

maximum displacement amplitude increased. The

displacement response of the mount stabilized after applying

several hundred cycles. After nucleation of the fatigue crack

and its subsequent growth to a critical size, the displacement

amplitude increased rapidly due to reduced stiffness and

failure occurred. The failure point was defined as the number

of cycles at which the displacement amplitude deviates

drastically (steep increase) from its gradual linear change in

semi-logarithmic scale. This is because of stiffness drop

resulting from presence of macro-crack(s).

The load-controlled fatigue tests resulted in fatigue lives

between about 19,000 cycles and 161,500 cycles, depending

on the applied load amplitude. Experimental life scatter was

within a factor of two between duplicate tests. Crack growth

constituted a significant part of the total fatigue life in all tests.

Also, by increasing the mean load or R ratio with the same

load amplitude, the total component life increased. This is the

same results observed in specimen testing of the same material

[21] where by increasing R ratio in filled natural rubber,

fatigue life increased. This is attributed to strain

crystallization. By applying a nonzero minimum strain, rubber

does not come back from crystalline state to amorphous

rubbery state. This crystalline state in which the polymer

chains are aligned highly in the loading direction increase

resistance to crack growth, resulting in longer fatigue life [21].

For investigating the effect of higher frequency on the

component life, one test with the frequency of 3 Hz was also

conducted to compare with the test at 1 Hz. The fatigue life

was similar to the lives at 1 Hz. The difference in life has been

observed to be small for filled natural rubber under isothermal

conditions for the frequency range of 10-3

to 50 Hz [26].

In order to evaluate the difference between load control (LC)

and displacement control (DC) on component fatigue life, one

axial test in DC was conducted based on midlife response

displacement amplitude and R ratio of the corresponding LC

test. The crack grew more rapidly under load control than

under displacement control (i.e. less crack nucleation life), but

the crack initiation location was the same. The total fatigue

lives in load control and displacement control were similar,

within a factor of two of each other.

Variable amplitude component uniaxial

fatigue tests

Four component fatigue tests were conducted in order to

evaluate the applicability of linear damage rule, rainflow

cycle-counting method, and life prediction methodology used

for variable amplitude loading of the cradle mount component.

Near zero load R ratio along with two load ranges of 3,000 N

and 3,600 N were used and each test was duplicated to

evaluate variability. A triangular waveform with 16.5 seconds

duration per block was used (see Figure 3). The same method

of storing data and defining failure as discussed above for

constant amplitude loading was also used here. In duplicate

tests, damage evolution of two of the mounts was monitored

by periodic visual inspection to define the crack initiation life

and crack growth.

Results showed the experimental life scatter to be within a

factor of two between duplicate tests. By increasing the load

range, the total life decreased and the ratio of crack initiation

life to total life decreased. Crack growth life was a significant

part of the total fatigue life, similar to the constant amplitude

component tests. Crack length was not a significant factor in

fatigue life, as even at a length of about 4 cm, the component

was still at only about half of its total life. However, crack

depth had a more important effect on life and when crack

depth was on the order of 3 cm, the component was near

failure. More details of these observations are presented in

[27].

Constant amplitude component

multiaxial fatigue tests

Cradle mount multiaxial tests were also performed. Axial

loading amplitude of 1100 N and R ~ 0 along with torsion

loading with amplitude of 30 N.m. and R = -1 were used in

these experiments. Two tests for each condition of both

in-phase and 90 out-of-phase tests were conducted. One of

the in-phase and one of the out-of-phase tests were stopped in

regular intervals to monitor cracking behavior. Both axial as

well as rotational displacement responses of each test

specimen were periodically recorded and failure was defined

by using the abovementioned method and also the lower

number of cycles at which the axial or rotational displacement

amplitudes increased drastically from its gradual linear change

in semi-logarithmic scale.

Experiments resulted in fatigue lives between about 21,500

cycles and 67,500 cycles. Results showed shorter life for 90°

out-of-phase loading, compared to in-phase loading. Fatigue

life scatter between duplicate tests within a factor of three for

in-phase tests and within a factor of two for out-of-phase tests

were observed. The results showed that crack growth life was

a significant portion of the total fatigue life (about 75%) for

in-phase test, while for out-of-phase test, this ratio was about

30%. Also crack length did not have a significant effect on

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fatigue life for in-phase loading, whereas crack depth had a

more dominant effect on life than crack length. For out-of-

phase loading, crack length was a key factor, rather than crack

depth. This could be because of the fact that in in-phase

loading, torsional and axial loading peaks are applied

simultaneously to the cradle mount, while this is not true for

out-of-phase loading. Due to phasing effect in out-of-phase

loading, the ratio of crack initiation life to total life increased

about 3 times, as compared to the same loading level for

in-phase condition.

IP and OP tests in displacement control were also performed

based on midlife displacements of the LC tests. The midlife

load-displacement and torque-rotation responses were similar

in both control mode tests. Crack initiation life was lower

under LC than under DC experiments. Crack initiation

location was the same for all tests, though. Similar to uniaxial

tests, the total fatigue life in load control and displacement

control were similar to each other.

Variable amplitude component multiaxial

fatigue tests

More complex loading conditions of variable amplitude

proportional and non-proportional axial-torsion were also

carried out on this vehicle component. Tests of

in-phase and out-of-phase were both conducted with two tests

of each condition. Loading condition was with the load range

of 3,680 N and with minimum load of near zero and torque

range of 50 N.m. with mean value of near zero. This is shown

in Figure 6. Results showed life scatter between duplicate tests

of within a factor of two for both in-phase and out-of-phase

loading conditions. Crack growth life constituted a significant

portion of the total life also in these tests. Crack depth was

shown to be a key factor in component fatigue life for in-phase

and out-of-phase tests rather than crack length. This was the

same observation as for constant amplitude uniaxial tests.

Figure 6. Variable amplitude in-phase and out-of-phase

axial-torsion loading history used for cradle mount testing.

LIFE PREDICTIONS

A cycle counting method and a cumulative damage rule are

necessary for damage calculations of variable amplitude

loading. The rainflow cycle counting procedure relates the

damage effect of variable amplitude loading to constant

amplitude loading. Miner’s linear damage rule which is the

most commonly used cumulative damage rule was also used in

this work, although load sequence or interaction effects

between cycles are not considered in this rule.

A damage quantification parameter is needed for life

calculations by relating the component multiaxial stresses and

strains to uniaxial specimen test and data. One of these

parameters is maximum normal strain as a critical plane

approach. Normal strain can be defined from:

1ˆ..ˆ)ˆ(

NCNeN

(1)

where C = FT F is the Green’s deformation tensor, F is the

deformation gradient tensor, and N̂ is the unit vector normal

to the plane in space. By using a MATLAB program, the value

and direction of maximum normal strain is defined on all

planes in space.

Another damage quantification parameter is cracking energy

density (CED). The increment in cracking energy density dWc

in the spatial description is defined in terms of the traction

vector T

and the unit displacement vector

d on a given

plane in the instantaneous deformed configuration and is given

by:

dTdWc . (2)

The normal to the plane is defined by the unit vector r

. By

converting from the spatial description to the material

description, the final expression for CED increment is given

by [28]:

RIER

RdESIERdW

T

T

c

)2(

~)2(

0

(3)

where /0 is the ratio of the deformed mass density (volume)

to the undeformed mass density (volume), F is the

deformation gradient, S~

is the 2nd

Piola-Kirchhoff stress

tensor, and E is the Green-Lagrange strain tensor. Equation 3

gives the cracking energy density in terms of the stress and

strain measures of the material description and in terms of a

unit vector in the undeformed configuration ( R

). SED (W)

and CED values are the same for simple tension uniaxial

loading, obtained by uniaxial specimen crack initiation tests

[21] and are given by:

Page 8 of 10

47.0)(148 fNW (4)

An efficient way to perform life predictions was found by

calculating cracking energy density (CED) on maximum

normal strain (MNS) plane. In this way, calculation of CED

history on MNS plane is performed only on a single plane,

once the critical plane with maximum MNS value is located

through a search algorithm. The effect of crack closure is

considered by using CED in this approach. This search

algorithm based on MNS is computationally efficient since

constitutive response is not needed or used to identify the

critical plane.

The correlation of predicted results with experimental results

for CED on MNS plane is shown in Figure 7. The results show

that using CED on MNS results in reasonably accurate crack

initiation life predictions for the complex loadings considered.

Therefore, this method can be considered a computationally

efficient approach to use for crack initiation life predictions.

Figure 7. Experimental initiation life versus predicted

component initiation life for all loading conditions

considered based on CED on MNS plane.

Although the life predictions shown in Figure 7 are for crack

initiation, as mentioned earlier crack growth constituted a

significant portion of the total fatigue life. Fracture mechanics

approach can be used for total fatigue life predictions utilizing

specimen crack growth data.

CONCLUSIONS

This study presented a generalized fatigue initiation life

prediction methodology and demonstrated the methodology

and its validation by using a cradle mount as a case study.

Based on the analysis presented and the component test

results, the following observations and conclusions can be

made:

1. Quasi-static FE simulations are shown to be applicable for

simulation of cyclic loading. The initial softening

associated with the Mullin’s effect is inherently

considered by using the stabilized cyclic deformation

curve. Component stiffness prediction results agreed well

with the experimental results.

2. The location of critical element for crack initiation from

FEA was identical to the observed crack initiation

location in all cradle mount fatigue tests.

3. Comparison of predicted versus experimental cradle

mount fatigue initiation lives for the complex variable

amplitude multiaxial loading conditions show satisfactory

life predictions based on the presented critical plane-

based life prediction methodology. In this methodology

the critical plane is the plane experiencing the largest

maximum normal strain. Cracking energy density (CED)

is then evaluated on this critical plane as a damage

quantifying parameter.

4. Life prediction results show that Miner’s linear damage

rule (LDR) and Rainflow cycle counting method

commonly used for metallic materials and components

are also applicable to fatigue life prediction of elastomeric

components.

5. Displacement-controlled and load-controlled component

tests at the same mid-life load and displacement levels

resulted in similar deformation response, crack initiation

location, and fatigue lives.

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ACKNOWLEDGMENTS

Funding of this study was provided by Chrysler Group LLC.

PAULSTRA provided the cradle mount component for the

study.

DEFINITIONS/ABBREVIATIONS

C Green deformation tensor

dWc increment in cracking

energy density

d unit displacement vector

E Green-Lagrange strain

tensor e strain

F deformation gradient

tensor f frequency

I Identity matrix

Nf cycles to failure

N̂ unit vector normal to the

plane

NE engineering strain

R minimum to maximum

load or strain ratio

R

unit vector in the

undeformed configuration

r

unit vector in the current

configuration

S~

2nd Piola-Kirchhoff stress

T Cauchy stress tensor

T

traction vector

Page 10 of 10

W strain energy density

mass density

A axial

CA constant amplitude

CED cracking energy density

DC displacement-controlled

FEA finite element analysis

IP in-phase

LC load-controlled

LDR linear damage rule

MNS maximum normal strain

OP out-of-phase

SED strain energy density

VA variable amplitude

CONTACT INFORMATION

Dr. Ali Fatemi

Distinguished Professor of Mechanical, Industrial and

Manufacturing Engineering, The University of Toledo

2801 W Bancroft Street, Toledo, OH 43606

Phone: (419) 530-8213

afatemi@eng.utoledo.edu