# Structural Analysis: How Do You Know If Your Part Will Fail?

SOLIDWORKS simulation provides a wide range of tools to simulate stress in mechanical parts. As with any simulation, the results are only as good as the assumptions we make when setting up the model and analyzing the results. This article focuses on the way we interpret the calculated stress to determine whether a part will fail.

Before we get into determining whether your part will fail, it’s important remember that this is only one aspect of a good stress analysis. It’s also vital that the boundary conditions and mesh realistically simulate the loading of your part.

The first question to ask is whether the boundary conditions accurately represent the way the part will be loaded. The mesh must be of sufficient quality to provide numerically accurate calculations. Aspect ratio is one important measure of mesh quality, this means that the triangular faces of elements should be as close to equilateral triangles as possible. Very elongated elements with high aspect ratios over 3 will reduce the accuracy of the simulation. Similarly, distorted elements, as measured by the Jacobian, may cause the simulation to fail.

Selecting Mesh Details from the context menu of the element in the simulation tree brings up useful information to evaluate mesh quality. Geometry should be simplified, and mesh controls should be added to achieve a reasonable mesh quality.

Another important consideration for the mesh is whether it has sufficient detail to provide the actual maximum stress with stress concentrations.

There can be something of a trade-off here between removing features to improve mesh quality and maintaining the features that will actually affect the result. This is somewhere that the skill and experience of a stress analyst can be very valuable.

Simulation using finite elements usually isn’t actually the best way to determine the peak stress within stress concentrations. It’s much better to use the FEA to determine the stress field surrounding the stress concentration, and then determine the actual peak stress using an analytical method. Formulas for a wide range of features and loading conditions can be found in reference books such as Roark’s Formulas for Stress and Strain, or Peterson’s Stress Concentration Factors.

This is a very brief overview of what’s required to perform a good stress analysis. So, assuming you have accurately determined the stress in the part, how do you know whether it will fail?

# Failure Criteria

Material failure may occur under static stress, fatigue or buckling. Under static stress conditions, materials generally fail in one of two ways, either by brittle failure (fracture) or by ductile failure (yield).

Mild steel is a typical example of a ductile material and ceramic is an example of a brittle material, although almost any material can behave in a brittle way under conditions such as very low temperature or highly cyclic loading. Similarly, most materials can be ductile at very high temperature. Over the full range of typical conditions, most materials can be considered to be either brittle or ductile. However, some materials, such as aluminium alloys, are a little less clear – a single large force is likely to result in yielding while a cyclic fatigue load will result in fracture.

The way that failure is defined may also vary according to the way a part is used. For example, if a shackle on a safety harness yields while arresting a fall, this probably doesn’t constitute a failure. In fact, it may be desirable for the shackle to yield, since this will dissipate some energy, protecting both inline equipment and the falling person from higher peak forces. [Hopefully, the shackle carries a warning that it should not be used after a fall, now that it has a shape different than its design shape. –Ed.]

In this case, a simple failure criterion could be when the average stress over its cross section exceeds the material’s ultimate tensile stress. However, if the same shackle was used as lifting gear, requiring repeated use, then yielding would be considered as a failure of the part. In this case, the same part, undergoing the same loading, can have different failure criteria – defined according to the usage requirements.

Some potential physical mechanisms for failure include yielding, fracture and buckling. A different analysis is required to check for each failure criteria.

For a part loaded in pure tension, the yield criterion is simply the yield stress for the material. However, most parts have more complex loadings, resulting in a three-dimensional combination of tension, compression and shear.

The simplest way to deal with this is to resolve the stresses into their principal directions, using Mohr’s circle. If these individual values are less than the material’s yield stress, this theory would assert that it shouldn’t fail. The principal stress approach is a simplification and other failure theories take a more sophisticated approach to determine when yield will occur. They consider the micro-mechanics of materials, involving atoms slipping within the crystal lattice and grain boundaries moving over each other.

Different approaches should, therefore, be used for ductile and brittle materials. They typically assume that a material is ductile and isotropic, meaning it has the same strength and stiffness in all directions. Metals can generally be considered to be isotropic, while wood and composites cannot.

The most common failure criteria used for static stress are von Mises, Tresca and maximum normal stress. They all involve first calculating principal stresses and then combining them into a single stress value that represents the stress at a point in the 3D solid. If this combined stress is less than the tensile yield stress for the material, it should not yield.

Von Mises and Tresca are used for ductile materials, while maximum normal stress is used for brittle materials. Von Mises is the most common, used for most static stress analysis. Tresca is very similar, but can give slightly higher stress values under certain circumstances; it is therefore more conservative, resulting in improved safety.

There is no stress plot listed as Tresca in SOLIDWORKS simulation but the Stress Intensity (P1-P3) gives the same values as Tresca.

For brittle materials, it is best to use the maximum principal stress (P1). However, brittle materials may require more detailed consideration of their fracture mechanics, which describes the way that cracks propagate and result in sudden and catastrophic failures.

Many theoretical failure criteria have been devised for brittle failure. The below plots show that for von Mises, Tresca and maximum principal stress, the results are very similar but slightly different maximum values are calculated.

In this article, I’ve given a quick overview of some of the most important failure criteria for failure under static stress.

It’s important to also check whether your part might fail under buckling or fatigue. In an ideal world, we would have clear rules for which failure criteria to apply for specific materials, loading conditions and functional requirements. Unfortunately, material science isn’t quite there yet. Instead, a number of different theories are in use and each has strengths and weaknesses.

Although a skilled analyst can consider relevant criteria for each case, ultimately no simulation can be considered an infallible way to determine whether a part will fail. Ultimately, testing is still required. Simulation, can however, dramatically reduce the number of design and test iterations.

Simulation is more useful for providing rich qualitative data showing stress fields than it is in predicting exact failure. This can be invaluable in assisting a designer, or optimization algorithm, to design parts which put material where it is needed to carry loads.