Maximum stress failure

In the maximum stress failure criterion, each and every one of the stresses in principal material coordinates must be less than the respective strengths otherwise, fracture is said to have occurred. That is, for tensile stresses,... 

Figure 2-37 Maximum Stress Failure Criterion (After Tsai [2-21])...

The maximum strain failure criterion is quite similar to the maximum stress failure criterion. However, here strains are limited rather than stresses. Specifically, the material is said to have failed if one or more of the following inequalities is not satisfied ... 

The only difference between the maximum strain failure criterion. Equation (2.125), and the maximum stress failure criterion, Equation (2.118), is the inclusion of Poisson s ratio terms in the maximum strain failure criterion. 

As with the maximum stress failure criterion, the maximum strain failure criterion can be plotted against available experimental results for uniaxial loading of an off-axis composite material. The discrepancies between experimental results and the prediction in Figure 2-38 are similar to, but even more pronounced than, those for the maximum stress failure criterion in Figure 2-37. Thus, the appropriate failure criterion for this E-glass-epoxy composite material still has not been found. 

One advantage of the maximum stress failure criterion is that it gives an indication of the type of failure mode. By checking which of Eqn (6.33) is satisfied, one can determine whether the fibers or the matrix failed and whether it is a tension, compression, or shear failure. Of course, this is a macroscopic assessment as the failure criterion in this form does not allow a more detailed determination of failure initiation. For example, a shear failure determined by the last of Eqn (6.33) cannot be traced down to a matrix failure due to local tension or compression nor can it be determined whether the matrix crack was parallel or perpendicular to the fibers. 

Another three-dimensional axisymmetric stress distribution for the stress around fiber breaks was obtained by Naim [93] using variational mechanics. In this study, breaks interaction was also included and it was assumed that both fiber and matrix were linearly elastic and a perfect adhesion at the fiber-matrix interface. To account for the stress singularity at the matrix crack tip of the fiber break, the matrix plastic-model was also included. Imperfect adhesion to mimic a failed fiber-matrix interface was added to this model to study the mechanism of interfacial failure, that is, the stress conditions that cause the extent of interfacial failure or its increase. It was suggested that due to the complexity of the multi-axial stress state, a simple maximum stress failure criterion was unrealistic and an energy release rate analysis was necessary to calculate the total energy release rate associated with the growth of interfacial damage. 

Solving for the uniaxial stress 0 c in terms of principal material stress components and applying the maximum stress failure theory constraints shown in Equation 9.9 gives the following five conditions that must be met for allowable stress For tension ... 

The following sections will describe methods used to calculate the stresses from each loading source. Using the maximum stress failure criterion, stress states of each ply of a laminate will be evaluated to determine whether or not cracking will occur. 

The maximum stress failure criterion is applied to investigate ply level damage related to transverse matrix cracking and longitudinal tensile and compressive failure. 

The strength of laminates is usually predicted from a combination of laminated plate theory and a failure criterion for the individual larnina. A general treatment of composite failure criteria is beyond the scope of the present discussion. Broadly, however, composite failure criteria are of two types noninteractive, such as maximum stress or maximum strain, in which the lamina is taken to fail when a critical value of stress or strain is reached parallel or transverse to the fibers in tension, compression, or shear or interactive, such as the Tsai-Hill or Tsai-Wu (1,7) type, in which failure is taken to be when some combination of stresses occurs. Generally, the ply materials do not have the same strengths in tension and compression, so that five-ply strengths must be deterrnined ... 

Subsection A This subsection contains the general requirements applicable to all materials and methods of construction. Design temperature and pressure are defined here, and the loadings to be considered in design are specified. For stress failure and yielding, this section of the code uses the maximum-stress theory of failure as its criterion. 

Part AD This part contains requirements for the design of vessels. The rules of Division 2 are based on the maximum-shear theoiy of failure for stress failure and yielding. Higher stresses are permitted when wind or earthquake loads are considered. Any rules for determining the need for fatigue analysis are given here. 

Corrosion Fatigue Limit—the maximum stress that a metal can endure without failure. This is determined in a stated number of stress applications under defined conditions of stressing and corrosion. 

If the fibres are aligned at 15° to the jc-direction, calculate what tensile value of Ox will cause failure according to (i) the Maximum Stress Criterion (ii) the Maximum Strain Criterion and (iii) the Tsai-Hill Criterion. The thickness of the composite is 1 mm. 

Determine whether failure would be expected to occur according to (a) the Maximum Stress (b) the Maximum Strain and (c) the Tsai-Hill criteria. 

A single ply glass/epoxy composite has the properties Usted below. If the fibres are aligned at 30° to the x-direction, determine the value of in-plane stresses, a, which would cause failure according to (a) the Maximum Stress criterion (b) the Maximum Strain criterion and (c) the Tsai-Hill criterion. 

A carbon/epoxy composite with the stacking arrangement [0/ - 30/30]j has the properties listed below. Determine the value of in-plane stress which would cause failure according to the (a) Maximum Strain (b) Maximum Stress and (c) Tsai-Hill criteria. 

The Tsai-Hill failure criterion appears to be much more applicable to failure prediction for this E-glass-epoxy composite material than either the maximum stress criterion or the maximum strain failure criterion. Other less obvious advantages of the Tsai-Hill failure criterion are ... 

For E-glass-epoxy, the Tsai-Hill failure criterion seems the most accurate of the criteria discussed. However, the applicability of a particular failure criterion depends on whether the material being studied is ductile or brittle. Other composite materials might be better treated with the maximum stress or the maximum strain criteria or even some other criterion. 

Interaction between failure modes is treated instead of separate criteria for failure like the maximum stress or maximum strain failure criteria. 

Identify which subcriterion for failure applies for each segment of the multiseg-mented maximum stress and maximum strain failure criteria cun/es in Figures 2-37 and 2-38 for uniaxial off-axis loading c . 

This is determined by applying a suitable design stress factor (factor of safety) to the maximum stress that the material could be expected to withstand without failure under standard test conditions. The design stress factor allows for any uncertainty in the design methods, the loading, the quality of the materials, and the workmanship. 

Figure 4.48. SN curve ofABS, examples of maximum stress S (MPa) versus number of cycles at failure (N)...

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