Topic

# Flow stress

About: Flow stress is a(n) research topic. Over the lifetime, 11089 publication(s) have been published within this topic receiving 289106 citation(s). The topic is also known as: yield stress & yield strength.

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Abstract: We show that the indentation size effect for crystalline materials can be accurately modeled using the concept of geometrically necessary dislocations. The model leads to the following characteristic form for the depth dependence of the hardness: H H 0 1+ h ∗ h where H is the hardness for a given depth of indentation, h, H0 is the hardness in the limit of infinite depth and h ∗ is a characteristic length that depends on the shape of the indenter, the shear modulus and H0. Indentation experiments on annealed (111) copper single crystals and cold worked polycrystalline copper show that this relation is well-obeyed. We also show that this relation describes the indentation size effect observed for single crystals of silver. We use this model to derive the following law for strain gradient plasticity: ( σ σ 0 ) 2 = 1 + l χ , where σ is the effective flow stress in the presence of a gradient, σ0 is the flow stress in the absence of a gradient, χ is the effective strain gradient and l a characteristic material length scale, which is, in turn, related to the flow stress of the material in the absence of a strain gradient, l ≈ b( μ σ 0 ) 2 . For materials characterized by the power law σ 0 = σ ref e 1 n , the above law can be recast in a form with a strain-independent material length scale l. ( builtσ σ ref ) 2 = e 2 n + l χ l = b( μ σ ref ) 2 = l ( σ 0 σ ref ) 2 . This law resembles the phenomenological law developed by Fleck and Hutchinson, with their phenomenological length scale interpreted in terms of measurable material parametersbl].

3,241 citations

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Abstract: The kinetics of glide at constant structure and the kinetics of structure evolution are correlated on the basis of various experimental observations in pure f.c.c. mono- and polycrystals. Two regimes of behavior are identified. In the initial regime, the Cottrell-Stokes law is satisfied, hardening is athermal, and a single structure parameter is adequate. With increasing importance of dynamic recovery, be it at large strains or at high temperatures, all of these simple assumptions break down. However, the proportionality between the flow stress and the square-root of the dislocation density holds, to a good approximation, over the entire regime; mild deviations arc primarily ascribed to differences between the various experimental techniques used. A phenomenological model is proposed, which incorporates the rate of dynamic recovery into the flow kinetics. It has been successful in matching many experimental data quantitatively.

1,793 citations

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Abstract: The Hall–Petch relation is discussed separately for the yield stress of undeformed polycrystalline metals and for the flow stress of deformed metals. Key structural parameters are the boundary spacing, between grain boundaries in the former case and between dislocation boundaries and high angle boundaries in the latter. An analysis of experimental data supports the Hall–Petch relation for undeformed metals over a grain size range from about 20 nm to hundreds of micrometers. For deformed metals, boundary strengthening is not a constant and the Hall–Petch relation must be modified.

1,441 citations

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Abstract: A mechanism-based theory of strain gradient plasticity (MSG) is proposed based on a multiscale framework linking the microscale notion of statistically stored and geometrically necessary dislocations to the mesoscale notion of plastic strain and strain gradient. This theory is motivated by our recent analysis of indentation experiments which strongly suggest a linear dependence of the square of plastic flow stress on strain gradient. While such linear dependence is predicted by the Taylor hardening model relating the flow stress to dislocation density, existing theories of strain gradient plasticity have failed to explain such behavior. We believe that a mesoscale theory of plasticity should not only be based on stress–strain behavior obtained from macroscopic mechanical tests, but should also draw information from micromechanical, gradient-dominant tests such as micro-indentation or nano-indentation. According to this viewpoint, we explore an alternative formulation of strain gradient plasticity in which the Taylor model is adopted as a founding principle. We distinguish the microscale at which dislocation interaction is considered from the mesoscale at which the plasticity theory is formulated. On the microscale, we assume that higher order stresses do not exist, that the square of flow stress increases linearly with the density of geometrically necessary dislocations, strictly following the Taylor model, and that the plastic flow retains the associative structure of conventional plasticity. On the mesoscale, the constitutive equations are constructed by averaging microscale plasticity laws over a representative cell. An expression for the effective strain gradient is obtained by considering models of geometrically necessary dislocations associated with bending, torsion and 2-D axisymmetric void growth. The new theory differs from all existing phenomenological theories in its mechanism-based guiding principles, although the mathematical structure is quite similar to the theory proposed by Fleck and Hutchinson. A detailed analysis of the new theory is presented in Part II of this paper.

1,405 citations

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Abstract: This paper examines the conditions for instability of plastic strain under plane stress for a material conforming to the Mises-Hencky yield condition and strain-hardening according to a unique relationship between root-mean-square values of shear stress (q) and incremental strain (δψ).
If, under fixed loading conditions, the material undergoes a strain increment which is consistent with the applied stress system, the conditions are stable or unstable according as the increment in representative yield stress is greater or less than the increment in representative induced stress.
The strain at which instability arises is found in terms of the biaxial stress ratio p2/p1 under different conditions of applied loading, and the effect is demonstrated of strain-hardening according to an empirical relation of the type q = c (a + ψ)n.
The analysis is also applied to certain cases of non-uniform stress distribution. In the case of the hydrostatic bulge results are obtained showing a critical thinning ranging from 26 per cent for a non-hardening material to about 45 per cent for typical strain-hardening materials, values in general agreement with experimental data. Conditions over the punch head in the pressing of a cylindrical shell are discussed but computations are not attempted.

1,400 citations