Failure criterion

The criterion for failure (conventional failure criterion) in all test methods is defined as the number of load application, Nf/jg, when the complex stiffness modulus, has decreased 

The classical criteria were conceived to describe the failure of isotropic, elastic-plastic solids. The physical content of the six principal criteria is in brief the following  

The maximum principle stress theory (Rankine s theory) states that the largest principle stress component, 03, in the material determines failure regardless of the value of normal or shearing stresses. The stability criterion is formulated as 

In this case a is considered a basic material property which can be determined from, for example, a tension test. In stress space the surface of failure according to 

The maximum elastic strain theory (St. Venant s theory) states that inception of failure is due if the largest local strain, 3, within the material exceeds somewhere a critical value e. The failure criterion, therefore, is derived as 

If a limiting octahedral shearing stress, r, is postulated as a failure criterion the same mathematical expression as in Eq. (3.9) is obtained with 

Most technical parts are loaded by a multl-axlal stress state caused by external loads acting on them. Whether this stress state leads to failure is judged using a suitable failure criterion - also known as a fracture-criterion or -hypothesis. With such a mathematical formulation of all possible stress states leading to failure, a multi-axial stress state Is reduced to a comparative stress by which the material is assumed to be loaded [107]. 

In this way, hard-to-measure shear resistance can be determined rather precisely by the mathematically simple shear stress criterion  

For plastics with different tensile rr,s and compression strengths rr,,  

Moreover, experience shows that the HMH criterion (criterion of greatest shape deformation work according to Huber, von Mises and Henky) also usually provides sufficiently precise results. Then comparative stress is  

Three-dimensionai faiiure diagrams interposed to consider the influence of time on the strength of plastics. Load duration to faiiure t, t2[107J 

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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 ... 

It is helpful to compare this with other, similar, failure criteria ... 

These failure criteria can be applied to single ply composites as illustrated in the following Examples. 

The simplified failure envelopes are not derived from physical theories of failure in which the actual physical processes that cause failure on a microscopic level are integrated to obtain a failure theory. We, instead, deal with phenomenological theories in which we ignore the actual failure mechanisms and concentrate on the gross macroscopic events of failure. Phenomenological theories are based on curve-fitting, so they are failure criteria and not theories of any kind (the term theory implies a formal derivation process). 

For each of the failure criteria, we will generate biaxial stresses by off-axis loading of a unidirectionally reinforced lamina. That is, the uniaxial off-axis stress at 0 to the fibers is transformed into biaxial stresses in the principal material coordinates as shown in Figure 2-35. From the stress-transformation equations in Figure 2-35, a uniaxial loading obviously cannot produce a state of mixed tension and compression in principal material coordinates. Thus, some other loading state must be applied to test any failure criterion against a condition of mixed tension and compression. 

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

The preceding biaxial failure criteria suffer from various inadequacies in their representation of experimental data. One obvious way to improve the correlation between a criterion and experiment is to increase the number of terms in the prediction equation. This increase in curvefitting ability plus the added feature of representing the various strengths in tensor form was used by Tsai and Wu [2-26]. In the process, a new strength definition is required to represent the interaction between stresses in two directions. 

Thus, the Tsai-Wu tensor failure criterion is obviously of more general character than the Tsai-Hill or Hoffman failure criteria. Specific advantages of the Tsai-Wu failure criterion include (1) invariance under rotation or redefinition of coordinates (2) transformation via known tensor-transformation laws (so data interpretation is eased) and (3) symmetry properties similar to those of the stiffnesses and compliances. Accordingly, the mathematical operations with this tensor failure criterion are well-known and relatively straightforward. 

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 . 

L. B. Greszczuk, Stress Concentrations and Failure Criteria for Orthotropic and Anisotropic Plates with Circular Openings, in Composite Materials Testing and Design (Second Conference), H. T. Corten (Chairman), Anaheim, California, 20-22 April 1971, ASTM STP 497, American Society for Testing and Materials, 1972, pp. 363-381 (reprinted with permission). 

Finally, failure analysis is the process of comparing actual performance with the desired performance. Thus, failure analysis is a nontrivial part of the structural design process. Facets of failure analysis including what failure means for a structure are addressed in Section 7.6 on Design Requirements and Design Failure Criteria. 

DESIGN REQUIREMENTS AND DESIGN FAILURE CRITERIA 7.6.1 Introduction... 

The area of design failure criteria impacts, and is a quantitative measure of, the success of a design. Fundamentally, design failure criteria are the statement of the design requirements. The manner in which individual laminae as well as laminates fail is but a part of design failure criteria. Failure of laminae and laminates, as in Chapters 2 and 4, is a fundamental portion of all strength-related failure criteria, but those failures are also determining factors in stiffness-related failure criteria. 

CA 63,17781 (1965) Proplnt failure characteristics were measured in uniaxial and biaxial stress states for poly butadiene acrylic acid and Nitroplastisol proplnts, and failure conditions were examined over a wide range of temps. The observed failure conditions were compared for various failure criteria, and it was found that a... 

Data were pooled from the TORO-1 and -2 studies for 48 week efficacy analyses (Nelson et al. 2005). These generally confirmed the 24 week findings and also demonstrated the durability of virological response - in both the enfuvirtide -h OB and OB only groups only about 7% of patients met virological failure criteria between 24 and 48 weeks. 

The unitized package protocol established similar numerical limits, but then added the definition of what constitutes a toxic amount of product for a 25 lb child. For aspirin, eight tablets were determined to be the realistic package failure criteria. The failure... 

It is important to double-check the failure criteria of specific vendors. For example, Panasonic SMD capacitors allow for a 30% fall in capacitance by the end of life. That means, for a 20% tolerance capacitor, you need to start with a nominal value 79% higher than your calculated value (also don t forget to account for the additional fall in capacitance at low temperatures). 

Filling Standard Test Ignition Source to BS 5852 Failure Criteria... 

Limits on absolute deformations are used when the there is a risk of a structural member (i.e. wall panel) impacting critical equipment. This limit has no direct relationship with failure criteria and may be greater or less than the displacement which causes failure. Member shrinkage limits are used to limit the amount of movement in member ends which are not restrained axially during lateral loading. 

Data and procedures presented in this section can be used in either approach. Time-independent approximations of failure criteria are presented to provide first-order estimates of fire consequences. Time-dependent criteria are also presented where specific scenarios warrant more detailed analysis. Most of the thermal criteria is presented in terms of heat flux, although some temperature criteria are also presented. A conservative methodology is presented to translate heat flux from a fire to surface temperature on a material target. 

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