lec11 - Yielding Under Multi-axial Stress 2.002 Mechanics...

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Yielding Under Multi-axial Stress 2.002 Mechanics and Materials II March 10,2004
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Uniaxial tension/compression: initial linear elastic response, as axial stress, σ , is increased up to the uniaxial “yield condition”: Suppose that, at some location in a body made of the same material, the state of stress is multi-axial, with cartesian components σ ij ; QUESTION: Will plastic deformation occur under this state of stress?
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Approach : we need to define a non-negative scalar, stress-valued function of [all] the stress components, such that it can consistently generalize the uniaxial yield criterion, | σ | < σ y Observation # 1 : pressure insensitivity of uniaxial yielding Suppose that a uniaxial test is performed under fixed superposed hydrostatic pressure, p, so the cartesian stress components are Plastic deformation is observed to commence when | σ | = σ y , essentially independent of the value of p This suggests that yielding is ~ independent of the mean normal stress given by Σ = ( σ 11 + 22 + 33 )/3
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lec11 - Yielding Under Multi-axial Stress 2.002 Mechanics...

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