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In mathematical terms, failure theory is expressed in the form of various failure criteria which are valid for specific materials. Failure criteria are functions in stress or strain space which separate "failed" states from "unfailed" states. A precise physical definition of a "failed" state is not easily quantified and several working ...
The Tsai–Wu failure criterion is a phenomenological material failure theory which is widely used for anisotropic composite materials which have different strengths in tension and compression. [1] The Tsai-Wu criterion predicts failure when the failure index in a laminate reaches 1.
The Tsai hill criterion is interactive, i.e. the stresses in different directions are not decoupled and do affect the failure simultaneously. [2] Furthermore, it is a failure mode independent criterion, as it does not predict the way in which the material will fail, as opposed to mode-dependent criteria such as the Hashin criterion, or the Puck ...
Prior to yield, material response can be assumed to be of a linear elastic, nonlinear elastic, or viscoelastic behavior. In materials science and engineering , the von Mises yield criterion is also formulated in terms of the von Mises stress or equivalent tensile stress , σ v {\displaystyle \sigma _{\text{v}}} .
The Christensen failure criterion is a material failure theory for isotropic materials that attempts to span the range from ductile to brittle materials. [1] It has a two-property form calibrated by the uniaxial tensile and compressive strengths T ( σ T ) {\displaystyle \left(\sigma _{T}\right)} and C ( σ C ) {\displaystyle \left(\sigma _{C ...
Within the branch of materials science known as material failure theory, the Goodman relation (also called a Goodman diagram, a Goodman-Haigh diagram, a Haigh diagram or a Haigh-Soderberg diagram) is an equation used to quantify the interaction of mean and alternating stresses on the fatigue life of a material. [1]
The Drucker–Prager yield criterion [1] is a pressure-dependent model for determining whether a material has failed or undergone plastic yielding. The criterion was introduced to deal with the plastic deformation of soils. It and its many variants have been applied to rock, concrete, polymers, foams, and other pressure-dependent materials.
Alternative failure criteria include Soderberg and Gerber. [36] As coupons sampled from a homogeneous frame will display a variation in their number of cycles to failure, the S-N curve should more properly be a Stress-Cycle-Probability (S-N-P) curve to capture the probability of failure after a given number of cycles of a certain stress.