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CHAPTER 5

FATIGUE FAILURE ANALYSIS OF A CHASSIS

5.1 INTRODUCTION

A premature failure occurs prior to the expected load cycles during

the vertical fatigue tests of a 50 to 60 ton chassis. To determine the reason of

the failure, a detailed A CAD model of the chassis was developed using Pro-E

and imported to the ANSYS in the form of IGS file format. Mechanical

properties of the chassis material were taken from the material data, to

determine fatigue strength calculation and standard data. Using these data,

stress and fatigue life analyses were performed using finite element method.

Fatigue crack initiation locations and minimum number of load cycles before

failure initiation were determined. Results provided from tests were compared

with the analyses. Design enhancement solutions were proposed to increase

the fatigue life of the chassis.

5.2 CHASSIS FATIGUE LIFE ANALYSIS

Fatigue failure analysis is to obtain stress and strain time history

about every node of the chassis, because the chassis finite element model has

a number of elements. In addition, the fatigue crack propagation of the chassis

has been determined. Consequently, the quasi-static stress analysis method

used for analyzing frame fatigue life can effectively simplify the simulation.

The load time history of mainly forced locations can be got from

ADAMS simulation. Tire reaction loads applied on the suspension mounting

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points. Based on the static condition, structure stress influence factor

corresponding to component load of endangered nodes can be got from the

simulation.

5.2.1 Fatigue Life Prediction

Since the chassis is actually loaded with dynamic forces during the

service, fatigue analysis was also performed. An estimation of the stress life

endurance limit is S'e = 0.504Su MPa.

Figure 5.1 S - N curve for fatigue and weld

Estimated S-N curves for ASTM A 572 - Gram 50, Normalized

High Strength Low-Alloy Structural Steel Plates. This represents the fatigue

strength at minimum 1 million cycles and more. Fatigue life prediction of the

chassis are 106 cycle strength, .9Su - bending, and .75Su for axial, the S–N

curve of the chassis material was estimated by means of a practical method 15

specimen tested.

S-N Curves for BWI

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This data has been obtained from the simple tensile tests from the

structural laboratory. S0e stands for the stress life endurance limit of ideal

laboratory samples. To predict the true fatigue strength Se for a chassis

material, S0e has to be multiplied by several modifying factors which

represent various design, manufacturing, and environmental influences on the

fatigue strength. Se is given as

Se = S'e*(ka*kb*kc*kd*ke*kf*k6)

where, Se - separate Fatigue strength (ksi)

S'e - endurance Limit (ksi)

Ka - surface Condition factor

Kb - size Modification factor

Kc - load Modification factor

Kd - temperature modification factor

Ke - reliability factor

Kf - miscellaneous-effects modification factor

k6 - stress concentration and notch sensitivity factor

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5.2.2 Fatigue Strength Calculation

Use only for pure torsional fatigue loading. When torsion is

combined with other stressed, such as bending, kc = 1 and the combined

loading is managed using the effective von Misses stress.

Table 5.3 Fatigue Strength Calculation

e = S'e*(ka*kb*kc*kd*ke*kf*k6) ka = aSub

Surface Finish A b ka, ksi ka, MPaSu, ksi Su, MPa Calculated

Ground 1.34 1.58 -0.085 0.934 0.934Machined or cold drawn

2.7 4.51 -0.265 0.876 0.877

Hot-rolled 14.4 57.7 -0.718 0.682 0.683As-forged 39.9 272 -0.995 0.58224 0.58126

Size factor, kb bending and torsion .11< d < 2 in 0.879d-0.107 0.808

2 < d < 10 in 0.91d-0.157 0.634 0.9 - test results for similar material

and size of part indicate that 0.9 is

reasonable

axial loading 1.000

Loading factor, kc bending 1axial 0.85torsion 0.59

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Table 5.4 Temperature Factor and Reliability Calculation

Temperature factor, kd 1 temp < 400

FReliability factor, ke

ke = 1-0.08*za Reliability, % Transformation

variate, za ke

50 0 1.00090 1.288 0.89795 1.645 0.86899 2.326 0.814

99.9 3.091 0.75399.99 3.719 0.702

99.999 4.265 0.65999.9999 4.753 0.620

Torsional stresses reduce the fatigue life from that observed with

completely reversed loading. The Goodman diagram, originally proposed in

1890, is a graphical representation of this effect.

a mean

FL u

S S 1S S

(5.1)

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Figure 5.2 Goodman graphical reprementation

The alternating stress is plotted on one axis and the mean stress on

the other. The allowable alternating stress with no mean stress is the fatigue

limit. The maximum mean stress, with zero alternating stress, is the ultimate

strength. A straight line is then drawn between the two points. Any

combination of mean and alternating stress on this line will have the same

fatigue life.

The safety factor has been determine the maximum strength of the

materials ensure a safe design. A single safety factor is applied to both the

stress amplitude and the mean stress.

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Table 5.5 Fatigue Stress Calculation

Miscellaneous-effects modification factor, kf Residual stress 0.8 0.9CorrosionElectrolytic plating 0.5 0.61Metal spraying 0.85Cyclic frequency Rottage corrosion 0.24 0.9

Fatigue stress – concentration factor, Kf k6 = 1/kf Kf = 1 + q*(kt-1) 1.84 0.543q 0.84 Su = 90 ksi kt 2 r >.12 in

kt 3 2 1.5

kf 2.68 1.84 1.42

Estimated rotating-beam endurance limit,S'e 0.504Su, ksi or MPa Su <= 212 ksi (1460

MPa)35.280

107, ksi Su > 212 ksi 107740, MPa Su > 1460 Mpa 740

Hence R nominal was computed as 198 MPa. Kt _ Kf is found as

1.181 and ke = 0.846. The S–N curve plotted regarding the modifying factors

was defined in the ANSYS_ Workbench V11.0 user interface. Stress-life

approach was used to determine the fatigue life of the chassis material.

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Table 5.6 Emprical factor calculation

Ka=ax(Su)b

Surface Finish a BSu, Psi Su, MPa

Ground 1.34 1.58 -0.085 Machined or Cold Drawn

2.7 4.51 -0.265

Hot Rolled 14.4 57.7 -0.718 As-Forged 39.9 27.2 -0.995

All fatigue analyses were performed according to infinite life criteria (N = 4 million cycles). Von Misses stresses obtained from finite element analyses are utilized in fatigue life calculations. Since the loading has a sinusoidal fluctuating characteristic (mean stress, Rm > 0), modified Goodman approach was used.

Figure 5.3 Notch sensitivity curve

ksi(

q)

Notch radius r (mm)

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Here, both R max corresponding to maximum 54500 kg and R min

matching a minimum 24500 kg of vertical load were obtained via FE analysis

and applied through body pad to the top of the rear rail structure. In the light

of the fatigue analysis results, it was estimated that crack initiation can occur

at the horse collar and rear rail structure region in the cycle time of 1,50,000

cycles, which is lower than the expected minimum fatigue life of 4,00,000

cycles. Here the obtained minimum value of n is 0.93. On the inner surface of

the shell, the minimum value of n was calculated as 0.767 at the region, where

the maximum stress concentration was observed. This means, at the region of

horse collar bottom and rear rail structure fatigue crack can initiate before 1.5

million load cycles, as observed in the vertical fatigue test.

5.3 FATIGUE LIFE ANALYSIS OF CHASSIS

A full scaled CAD model of chassis was prepared for the analysis

as shown in Figure 5.4. The chassis essentially consists of a bumper, front rail

structure, a horse collar, and a rear rail structure and rear axle. These parts are

welded properly two equivalent thin walled shells, which have a fabricated

box structure and casting. Box structure welded with a back up bar. Two rail

structures are connected with torque tube and horse collar assembly to

increase rigidity.

It consists of bumper which is at the front side of the truck. Front

rail structure is located at next to the bumper. Horse collar which is the

portion at the middle of the chassis, it carries engine and suspension system.

Rear torque tube structure is used to join left and right side of the rail

structure and also to withstand the load while vehicle is in torsion and

cornering cases. Body pad fitted on the chassis to sit the body and payload.

Finally, rear rail structure used to mount the rear axle and suspension of the

chassis.

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Figure 5.4 Chassis model for Fatigue life analysis

The solid model of the chassis was composed via Pro-E Version5.

CAD model of the complete chassis was imported into ANSYS pre

processing environment to constitute the FE model required in the analyses.

The FE model used in stress and fatigue analyses is shown in Figure 5.5. To

build the finite element model, chassis was meshed using SOLID 45, tetra

element a higher order three-dimensional solid tetra element, which has a

quadratic displacement behavior and is well suited to model irregular meshes.

The element is defined by 10 nodes having three translational DOF at each

node. FE model consisted of 79,305 elements and 2, 87,354 nodes.

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Figure 5.5 Chassis meshed Model

5.3.1 Fatigue Boundary Condition

Four different fatigue load cases have been evaluated as for the

maximum load cases. The vertical fatigue load case was found to be the most

severe and was also in the same area as before that is of interest, with loading

conditions as shown in Figure 5.6. We see that fatigue life range

perpendicular to the weld, located in the lower side of the horse collar portion.

It is in the order of 307 Mpa. For all fatigue load cases considered, this area is

the most critical.

Load applied to the FE model was chosen according to the loading

range used during the vertical fatigue test. For fatigue analysis, body weight

and payload can be applied on the top of the body pad and tire reaction load

can be applied on the suspension mounting points to Satisfy the equation of

equilibrium conditions.

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Figure 5.6 Bending load condition

5.3.2 Total Deformation of the Chassis

Figure 5.7 shows the total deformation of the chassis and it

indicates clearly that the deformation is maximum at the rear end of the

chassis. The numerical value of the chassis is 18 mm. Colour distribution of

the plot gradually was found to be decreased from rear rail to the front,

maximum level to the minimum level throughout the chassis. gradient

distribution in the direction of axial and lateral.

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Figure 5.7 Total deformation of bending

5.3.3 Von-misses Stress Distribution on the Chassis

Figure 5.8 shows the Von-misses stress in the behaviour which can

be obtained for the lateral and longitudinal direction in the both bending and

torsion cases. Bending stresses indicates for both front wheels and rear wheel

gets move upward direction. Stress distribution on the rear rail structure

179.3 MPa, with in the recommended value, maximum shear stress of the

chassis as shown in Figure 5.9.

Figure 5.7a S-N Curve Average Value

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Figure 5.8 Von-misses stress of the chassis

Figure 5.9 Maximum shear stress of bending

Figure 5.10 Fatigue life of bending load

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Maximum Fatigue life of the chassis was obtained as 31025 at the

critical region. This means, that the use of the additional plates and gusset

structure decreases stress concentration. By increasing the thickness of the

plate, it is possible to obtain enhanced rigidity.

Figure 5.11 Safety factors of the chassis

The static and fatigue analyses were composed according to this

change in the plate sized shape. However, analyses pointed out that this

increase on its own enhances the fatigue life of the chassis to a certain extent,

which is not sufficient enough to obtain the desired load cycles of 3.5 million

cycles. Therefore, plate thickness increase may be applied together with the

redesign of the chassis geometry as shown in Figure 5.10.

Safety factor of bending and torsion load is greater than 1 as shown

in Figure 5.11.

5.3.4 Fatigue Life of the Torsion Analysis

Additional stiffeners in the transition area, results in a better

distribution of the stresses. The magnitudes of the stresses are reduced. The

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stresses are reduced and distributed more evenly and are now in the order of

31025 fatigue life. More work and innovative solutions most likely to bring in

further improvements of this critical area.

Figure 5.12a Torsion left ramp loading

Figure 5.12b Torsion right ramp loading

This Figures 5.12(a), 5.12(b) clearly shows that the torsion

deformation and torsion stress on the modified chassis got greater than the

bending. Also, it can be seen that the maximum torsion stress of the two case

studies occurs near horse collar and rear rail structure of the chassis.

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Figure 5.13a Torsional deformation of left ramping

Figure 5.13b Torsional deformation of right ramping

Maximum Torsional deformation for both lamp and right ramp

cases. deformation on both the ramps are 13 mm at the rear suspension

mounting point on the chassis. Figures 5.13(a), 5.13(b) shows the

displacements in the X and Y direction for the both left ramp and right ramp

loading conditions. A similar behaviour can be obtained for the displacement

in the both left ramp and right ramp cases.

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Figure 5.14a Von-misses Stress of Bending Load

Figure 5.14b Von-misses Stress of Torsion Load

Figures 5.14(a), 5.14(b) shows the Von-misses stress in the

behaviour can be obtained for the lateral and longitudinal direction in the both

bending and torsion cases. Indicates torsional stresses for both left and right

ramp conditions move cross wise up and downward directions alternatively.

Stress distribution on the rear rail structure 224.2 MPa.

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Figure 5.15a Fatigue Life of the Chassis (Bending load)

Figure 5.15b Fatigue Life of the Chassis (Torsion load)

By means of FE analysis, Figures 5.15(a), 5.15(b) shows the fatigue life of the chassis torsion load was observed that there are stress concentrated regions on rear rail and horse collar portion areas; In addition to the modifying factors mentioned, a fatigue strength modifying factor ke must be taken into account by means of the static stress concentration factor Kt that is related to fatigue stress concentration factor Kf. Hence ke is calculated as ke ¼ = 1 Kf. For safety reasons, Kf can be assumed as to be equal to Kt, because of the dimensions and shape complexity of the chassis Kt cannot be derived from data in the standard literature. On the other hand Kt is defined as Kt ¼ r peak R nominal stress where R peak is the peak stress and at the root of the notch and R nominal the nominal stress which would be present. To calculate R

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nominal, the rear rail structure was assumed as a simple box section form which has a varying cross-section of critical region along the axis parallel to the neutral axis. Longitudinal axis Z direction is pure bending. Nominal stress was computed as shown in figure as R nominal ¼ M Z where M is bending moment and Z is the section modulus of the critical cross-section. The maximum principal stress about X - axis has been cleared in Figures 5.16(a), 5.16(b) for the both cases of ramping conditions. While the behaviour of the maximum principal stress is approximately same for the both bending and torsion cases.

Figure 5.16a Maximum Principal Stress of Fatigue Analysis (Bending)

Figure 5.16b Maximum Principal Stress of Fatigue Analysis (Torsion)

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The maximum safety factor shows that above the unity value. Difference in the displacements and stresses about the neutral axis of the chassis, It gets higher Y-axis for the two case studies. Higher rotational displacement is obtained when of both rear wheels gets over the ramp. The maximum Ry is occur near horse collar for the case of both rear wheels over the ramp, while the maximum Ry is occur near rear rail structure at the end for the case of one rear wheel get over the ramp. The results of the displacement an stress about the Z - axis were expressed in Figures 5.17(a) and 5.17(b).

Figure 5.17a Safety Factors of the Chassis (Bending load)

Figure 5.17b Safety Factors of the Chassis (Torsion load)

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The maximum Rz is occur between horse collar and the end of the

rear rail structure. The results of the dynamic simulation are expressed from

Figures 5.17(a) 5.17(b). The dynamic behaviour for the torsion stress in the

case of both bending and torsion rear wheels gets on the ramp

Figure 5.18a Stress Ratio of the Figure 5.18b Stress Ratio of the

chassis (bending) (torsion)

In Figures 5.18(a), 5.18(b) the behaviour of the torsion stress ratio

can be compared with the behaviour of the torsion stress of the chassis and its

behaviour shows good compatibility with the behaviour of reference.

5.4 RESULTS AND DISCUSSION

FE analyses showed that the regions, where fatigue failure was

initiated during vertical fatigue tests, are subjected to stress concentration,

which can cause a premature failure before the predicted 4 million cycles. The

results are in agreement with the results of vertical fatigue tests. Enhancement

of the fatigue life of the chassis is dependent on the decrease of the stress

concentration. The simplest way to reduce the stress concentration and

improve the fatigue life is to increase the thickness of the chassis box

structure. However, except regions front rail structure to satisfy the fatigue

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life criteria. Due to increase the plate thickness of front rail structure causes

slightly increase the weight of the chassis. The transition geometry may be

redesigned. Smoother transition geometry may offer an enhanced fatigue life

without any weight increase. In addition, shape of the reinforcement plate also

affects the stress concentration. As per the study of design, conclude that the

thickness of the plate were between 6mm to 25mm.

Premature fatigue failure of a truck chassis prototype was

investigated by using finite element analysis. Stress concentrated regions were

predicted at the rear rail structure of the chassis. The regions in which the

fatigue cracks originated were well-matched with the results of the analyses.

By using FE analysis the location of the failure can be predicted. Critical

regions determined are subjected to a combined steady and cyclic tensile

stress. The crack causing fracture is initiated at the stress concentrated regions

of the chassis. Although the chassis prototype satisfies the static endurance

condition for the maximum vertical load, analyses showed that premature

fatigue failure can occur prior to the predicted less than 3.5 million cycle’s

limit, if this load is applied in a cyclic manner. FE analyses also enable to

provide an estimation of the number of cycles before fatigue failure initiation.

To increasing the thickness of the rear rail structure plate similarly to maintain

the power to weight ratio of the total vehicle. An application including both

redesigning of the chassis area and increasing the thickness of the plate to

obtain a longer fatigue life, which can satisfy minimum design criteria.

5.5 CONCLUSION

Finite element analysis and tests can effectively solve the fatigue

life analysis of chassis. Actually, it is necessary to get some data based on

practical mine road surface so that there is some evidence to ensure the

accuracy of results. The multi body dynamic analysis provides effective load

conditions for static stress analysis and fatigue life analysis of chassis.

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According to the comparison of simulated stress and tested stress, the validity

of finite element model is completely ensured. Based on the quasi-static stress

analysis method, the fatigue life of the whole frame is obtained areas of horse

collar and rear rail structure are mainly low fatigue life.1.03e6 cycles, which

is located at the chassis suspension joint of front and rear rail structure. The

implementation of extra high strength structural steel offers big advantages in

terms of improved pay load and reduce manufacturing cost. From FE-analysis

it is shown that most of the chassis rear rail structure, torque tube and horse

collar portion. It is recommended that modification and redesigns are made in

order to improve the fatigue performances and efficiency.