7/28/2019 Facts About Von Mises Failure Criterion

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Facts about von Mises Failure Criterion, its Importance and Application

We need a failure criterion since the material test results are determined from unidirectional

tests only and which gives the Yield Stress as the maximum stress beyond which the

permanent (or plastic) strain sets in; but the real state of stress in a 3-D situation is multi

directional (defined by second-order stress tensor), and we need to somehow decide on thesafety of the structure based on some strength criterion based on one-dimensional yield

strength of the material. Pl. note that the yield stress is clearly demarcated only for some

ductile metallic materials like Steel, but for materials like Copper and Al-Copper alloys

(extensively used in aircraft industry) no such clear yield point exists, where we identify the

yield stress as that corresponding to 0.2% strain value (I found some discussions mentioning

about 5% strain! We need to have a physical feeling about quantities, not just numbers).

Many failure theories were proposed which is history; but among them the von Mises Failure

Criterion was established by test results as the best among them for predicting the failure of

ductile materials where the predicted failure stress agrees well with test values. What are the

reasons behind It and the basis for it?

It was observed that the Hydrostatic Stress (HS) State had no influence on the yield stress in

a structure; simply what it means is whether you apply unit HS or 100,000 units of HS the

yield point would remain the same! The total stress state (or stress tensor) at any material

point can be decomposed into Hydrostatic stress tensor and Deviatoric stress tensor whose

sum gives the total stress tensor. The HS component would result only in the volume change

or volumetric strain and does not distort the material. In contrast, the Deviatoric component

only distorts the material resulting in only shearing strain but would not result in volumetric

strain (The Deviatoric stress tensor has zero value for first stress invariant, and hence

represents a state of pure shear). In fact, decomposing the stress tensor at any material

point is equivalent to considering the stress tensor on Octahedral Planes, OHPs, (which are

panes equally inclined to principal planes) the Deviatoric stress tensor represents pure

state of shear on OHPs.

These observations led to postulate, (first Hankey and then by von Mises) that only the

distortion of the material would lead to the failure of the ductile metallic materials, and the

volumetric strain wold not influence the failure. Thus, the distortion strain energy was

calculated by subtracting the volumetric strain energy from the total strain energy, and

postulating that the material would fail when the distortion energy in 3-D stress state would

reach a value of the distortion energy in the 1-D stress state at the point of yield. The

equivalent stress value thus calculated from such an equality was referred to as von Misesstress, vMS, (or should be really Hankey-von Mises) stress for historical reasons. In fact, von

Mises stress formula contains terms with difference of principal stresses only and shows that

it would depend on the shear stress components only. Thus vMS is an equivalent stress

(and has stress units, and not just an index as some seem to suggest) and is always

positive. We say a material at any point has failed from strength consideration if the vMs at

that point reaches or exceeds the yield stress of the material. The experimental data on

structural failure showed that the failure stress predicted based on vMS was very close to

the failure stress observed in ductile metallic materials, and hence the universal use of von

Mises Failure criterion for ductile materials.