failure mode and strength predictions of anisotropic

7/30/2019 Failure Mode and Strength Predictions of Anisotropic

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Failure Mode and Strength Predictions of

Anisotropic Bolt Bearing Specimens

J. P. WASZCZAKAND T.A. CRUSE, Department of Mechanical Engineering,Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213

(ReceivedApril 6, 1971)

Amajor consideration in the design of a structure made of composite materi-als is the bolted joint since a bolted joint in a composite material has a significantlylower efficiency than the same joint in metals. Furthermore, the composite jointmay fail in unique modes not found in metal joints.

This study, in an attempt to further understand the failure characteristics ofsuch bolted joints, investigates the stress concentrations induced in anisotropicplates loaded by means of a single fastener. The development of a predictioncapability for both failure mode and ultimate load is the major goal of the earlypart of this work. Such a capability would allow synthesis rather than analysis tobe used in the future

designof fastener

joints.An

implied goalin this

studyis a

relative evaluation of the three proposed anisotropic failure criterion: maximumstress, maximum strain, and distortional energy.

COMPUTER SIMULATION

Aconstant strain, finite element computer program modified to handle aniso-

tropic composite materials [1]was used for the stress analysis. Only speciallyorthotropic laminates, i.e. laminates which are mid-plane symmetric and are cross-

plied, were investigated since the published data on bolt bearing specimens is alsolimited to this class of laminates. The bolt bearing test specimen contains two lines

of specimen symmetry as shown in Figure 1. Thus itwas

only necessary to in-clude one-fourth of the specimen in the finite element simulation. The grid repre-sentation used contains 480 triangular elements and 279 nodes.Acosine distribution of normal stress acting over the upper half of the hole

surface was used to simulate the resulting stress distribution caused by the bolt.The interaction was assumed to be frictionless. Bickley [2] shows this to be anexcellent approximation for isotropic bolt bearing specimens. Several isotropicbolt bearing test specimens were simulated using the cosine distribution of normalstress and the grid mesh previously described. The computed stress concentrationfactors for these specimens agreed with [3] to within six percent.

Finally,two other normal distributions of stress

significantlydifferent from the

cosine distribution (see Figure 2) were used to simulate the bolt-specimen inter-face stress boundary condition. The net force in the load direction in each casewas equal. It was observed that significant variation about the cosine distribution

J. COMPOSITE MATERIALS, Vol. 5 (July 1971), p. 421


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Figure 1. Bolt bearing test specimen.

resulted in insignificant alterations of the calculated stress fields for the specimenconsidered.

ANALYSIS PROCEDUREAND RESULTS

The selection of specimen geometries for the investigation was made from datawhich has been published by General Dynamics, NorthAmerican Rockwell andGrummanAerospace. Figure 3 illustrates the various failure modes included inthis

investigation.Astrength analysis of a laminated composite structure is based on the strengthsof its individual laminae. Lamina failure may be predicted to occur by the dis-tortional energy failure criterion [4] when the following combination of laminaprincipal stress ratios add to a number greater than or equal to one:

The maximum stress (or strain) failure criterion, on the other hand, requires thatthe ratio of principal stresses (or strains) to their respective ultimate stresses (orstrains) be greater than or equal to one for failure to occur.

The distortional energy failure criterion has been found in this study to be the

only reliable means of predicting bolt bearing specimen failure modes. Interpreta-tion of the maximum stress and maximum strain failure criteria, in an attempt to

predict specimen failure modes, has been very unsuccessful. The difficulty resultsfrom the anisotropy of the composite material. Figure 4 shows distortional energycontour plots for the main load carrying lamina in various experimentally failed

specimens.An initial application of the experimentally determined failure loadwas applied in each case. The contour plots were suflicient to enable the predic-tion of failure modes in all but the shear-out cases. For these specimens it was

necessary to consider the ratios of lamina principal stresses to their respective


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Figure 2. Variations about the cosine distri-bution of normal stress.

Figure 3. Bolt bearing test specimenfailure modes.

Figure 4. Distortional energy contour plotsfor bolt bearing specimens.


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ultimate stresses in the regions of high distortional energy to differentiate betweena shear-out mode and a bending tear-out mode.

Prediction of failure load was also based on normalized distortional energies.The values of DIST in the first row of circumferential elements around the holewere considered for each lamina.Asuccessive failure analysis was used to predictultimate load.As soon as an element in any given lamina achieved a value of DIST

equal to 1.0 that lamina was assumed to have failed and was removed from thelaminate. The load was then redistributed among the remaining laminae and allvalues of DIST were recalculated. If all recalculated vaules of DIST were less than

1.0 more load was applied until another lamina reached failure. This process was

repeated until total laminate failure occurred.The resulting predictions of failure load, based on distortional energies, were

conservative

(seeTable

I).The

degreeof conservatism varied with failure mode,

but more importantly it appeared to be a function of specimen anisotropy. Notethat the predicted failure loads for the net tension specimens improve greatly asthe percentage of 45laminae decreases. This same type of behavior was re-

ported by GrummanAerospace in a study they performed on laminate tensiondata. Both the maximum stress failure criterion and the maximum strain failure

criterion underpredicted one specimen ultimate load. However, failure load pre-dictions made using the maximum stress failure criterion are in agreement withthose of the distortional energy failure criterion to within about ten percent. The

major disadvantage encountered with the maximum stress criterion, as previouslystated, is its inability to clearly indicate failure modes.

The experimentally failed specimens exhibit excellent agreement with thepredicted failure behavior of this study. For example, a specimen which failed ina shear-out mode exhibited a relatively smooth, clean fracture surface. The dis-tortional energy contour plot for this specimen is shown in Figure 4 ( b ) . The regionof high distortional energy results from very high principal shear stress ratios which

Table 1.

Nomenclature T Tension G/E Graphite-Epoxy

C Combination 3/E Boron-EpoxyS Shear-Out

B Bearlna


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would lead to rather smooth shear fracture surfaces. On the other hand, a ( 0 /90/45) specimen which failed in a bending tear-out failure mode exhibiteda very coarse, jagged fracture surface along lines at 45. This behavior is againexpected from the computed stress ratios.Along lines at 45, where the dis-tortional energies are high, the largest stress ratios act in the first principal direction.These are the stresses which are trying to break fibers in tension.As a result, as the

triangular section is being torn away from the specimen, the fibers along these linesare being broken in tension; resulting in a very coarse, jagged fracture surface.

Another interesting feature of most of the experimentally failed specimens wasthe presence of a highly localized region of laminate destruction at the bolt-speci-men interface. This damage occurred in conjunction with almost every type of

experimental failure mode and was predicted by the stress analysis, Figure 4.

REFERENCES

1. J. E.Ashton, J. C. Halpin, and P. H. Petit, Primer on Composite Materials: Analysis,Technomic (1969).

2. W Bickley, "The Distribution of Stress Round a Circular Hole in a Plate", Phil. Trans.Roy. Soc.,A(London), Vol. 227 (1928), p. 383.

3. R. E. Peterson, Stress Concentration Design Factors, Wiley (1953).4. S. W. Tsai, "Mechanics of Composite Materials, Part IITheoretical Aspects",Air

Force Materials Laboratory Technical ReportAFML-TR-66-149 (1966).

failure mode and strength predictions of anisotropic

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