Educational Background Article

Copyright (C) 2014 F.A.Conle and Univ. of Waterloo

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the loading is from a variety of independent sources is more involved than the

approximations described in

Case 1.

The independence of the load histories makes it very difficult to adopt one

"worst case" load set to impose on a finite element model. A wide variety of

load sets may need to be analyzed in order to find the critical stress states

of elements. On simple components with only a few load "channels" it may be

possible to determine the significant load cases. On a structure such as an

automobile where the significant loads are buried in one or two hour recordings

from the proving grounds, and the number of independent load channels may

approach 100, the process needs to be automated (Refs.:[1,2]). The process

used is similar to that known as "Influence Factor Analysis" used for many

years in bridge construction, and the individual steps needed by the analyst

are fairly simple, but computationally intensive. An outline of the process

is given in the following sections.

determined by analysis using dynamic models such as ADAMS, from laboratory testing,

from measurements of previous prototypes, or from direct measurements from

the proving ground events. A front lower arm bushing as indicated in Fig.1

may have three forces and one or more moments as load inputs (only 3 forces are

shown).

**Fig. 1: **

For many vehicles similar to the one shown of a car "body in white" there are sixty

or more load or moment vectors applied to the body.

The load for each variable is calibrated to known laboratory inputs and observed using

load cells or strain gages on the body or the suspension component. With all load

channels calibrated the vehicle is subjected to the expected customer load history;

often by driving the vehicle over severe proving ground events. A typical data set

may be 80 channels of forces recorded at 1000 samples/sec/channel for a period

of one or two hours. All data points must be synchronized in time for a proper

analysis. For the conditions mentioned above the file size using (2byte data points)

works out to be slightly larger than 1_Gbyte.

2_million shell elements. Elements typically are shells to simplify subsequent element stress

post processing for fatigue. Components that require solid elements can be "masked" on

the outer free surface with very thin shells, assuming that the fatigue critical location

is on the surface, to achieve the same stress simplicity. For fatigue purposes generally,

elastic analysis is sufficient if the fatigue post-processing performs a Neuber type[3]

plasticity correction.

it becomes expedient to reduce the size of the problem by automatically selecting only

the most critical elements with the highest expected stresses. One method of excluding

elements that are of low stress is to run all the elements with a very short load

history. A reasonable way to obtain a short but "representative" load history is to

scan all points in all channels for their max and min values. At each channels max and

**Fig. 2: ** Computation of the Simultaneous Maxima for each Load Channel

min points (shown in red in Fig. 2) all the other channel values at the same instance of

time (shown in green) are also saved. Such a table is termed a simultaneous max-min list.

The procedure is expanded somewhat to the top five (or some other number) maxima of each

channel. The simultaneous max/min list of loads is the run through the superposition

process described below for all elements. From these shortened history predictions

the top 10,000 (or some other number) critical fatigue elements are selected for

subsequent analysis using the full load histories.

individual load case. Given a set of 80 load channels this implies that 80

finite element analyses are performed, each with only one unit load for a given

channel. For each element this results in a list of 80 x 3 unit load influence

factors for Sxx, Syy and Sxy as sketched in Fig. 3 for two example channels.

**Fig. 3: **

The principle of elastic superposition is then applied for each element by stepping

through the histories of loads, and for each time step point multiplying the unit

load factors by the instantaneous load value. As depicted in Fig. 4 the stress

values for each load channel are then summed to give the stress state for that

element at that point in time.

**Fig. 4: **An example of stress superposition for a given element.

stresses in the X and Y axis terms. Fatigue failure, however, will often occur

perpendicular to the direction of maximum tensile stress or, more specifically,

the maximum fluctuation of stress with the largest tensile mean value. There are

a number of ways to compute such a critical plane ( see Ref. [Chu]), but here

only one variation is explained. The process uses the Sxx, Syy and Sxy stresses

at all computed points to find the first and second principle stresses, S1 and S2

and their direction of action. As shown in Fig. 5.

**Fig. 5: **

Values computed for S1 and S2 and their associated angles from the X axis are

plotted in a matrix of occurrences as shown in the middle of the figure for a short

load history. Angles are divided into 10 degree intervals. The angle interval

with the largest stress fluctuation (or some other criterion) is then selected to

be the direction with the most fatigue damage. A cut is then assumed in the

element at 90 degrees to this critical direction and the stress history ( Sn )

on that plane is computed with subsequent Rainflow cycle counting and a uniaxial

fatigue analysis.

stress directions etc to a PATRAN or other type file for graphical display.

The fatigue analysis for a given element, however, is computed by the same

uniaxial fatigue life calculation program such as saefcalc2.f.

Computationally this would be the most expedient, but other programs such as

a crack propagation program could also be applied.

- [1] F.A.Conle and C.W.Mousseau, "Using vehicle dynamics simulations and

finite-element results to generate fatigue life contours for chassis

components," Int. J. Fatigue, V 13, N3, 1991, pp.195-205.

- [2] H.Agrawal, A.Conle, et al."Upfront Durability CAE Analysis for

Automotive Sheet Metal Structures, SAE Paper 961053, Feb. 1996.

- [3] C.-C. Chu, "Multiaxial fatigue life prediction method in the ground

vehicle industry," Int. J. Fatigue V 19, Supplement N1, 1996, pp.S325-S330.

- [4] C.C. Chu, F.A.Conle, A.Huebner, "An Integrated Uniaxial and Multiaxial

Fatigue Life Prediction Method," VDI Bericht Nr. 1283 1996, pp.337-348.

- [5] "SAE Fatigue Design Handbook," SAE AE-22, 1997 ISBN 1-56091-917-5

- [6] "Mulatiaxial Fatigue of an Induction Haredened Shaft," SAE AE-28,

Editors: T.Cordes and K.Lease, 1999, ISBN 0-7680-0528-0

- -
- Various commercial versions: