Dynamic Plasticity by N. Cristescu

By N. Cristescu

This booklet provides a self-contained and complete examine the sector of dynamic plasticity for researchers and graduates in mechanical engineering. Drawing at the author's lengthy occupation within the box, the booklet drastically extends fabric from the 1967 unique variation with the addition of unpolluted examine chapters in addition to an entire creation to the common conception of plasticity.

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2. For the Tresca condition the relationship between the yield stresses in shear and tension is 2τY = σY . 6. 5 in) 10:41 22 Dynamic Plasticity The Mises [1913] Yield Condition. The von Mises yield condition is expressed as IIσ = k 2 , where IIσ = = 1 2 2 2 [(σ11 − σ22 )2 + (σ22 − σ33 )2 + (σ33 − σ11 )2 ] + σ12 + σ23 + σ31 6 1 [(σ )2 + (σ2 )2 + (σ3 )2 ] . 2 1 The von Mises yield condition is represented in the three axial stress space as a circular cylinder shown in the last two figures. For the plane case it is an ellipse.

5 in) 10:41 44 dynamic Dynamic Plasticity nˆ v P V dS S Fig. 1 The reference volume in space. 3) or in vector form dρ + ρ div v = 0 . 3a) dt That is the continuity equation due to Euler in 1757. 4) which is the condition of incompressibility. The continuity condition can be written in material form. If V is the volume of material at time t, and V0 the volume at the same material at time t0 , we have (Fig. 2) ρ(X, t0 ) dV0 = V0 ρ(x, t) dV = V ρ(x(X, t), t)|J| dV0 V0 with |J| the absolute value of the Jacobian determinant J≡ ∂x ∂X ∂x ∂Y ∂x ∂Z ∂y ∂X ∂y ∂Y ∂y .

The quantities Ac and Af are constants with no dimension and of the dimension of stress, respectively. , Af , is reached. The model is slightly changed to describe various effects, as: relaxation, the cyclic Swift effect, the pre-necking and post-necking relaxation, creep, free-end torsion, rate-dependent deformation behavior of metals and solid polymers, high temperature applications, etc. 13 Rate Type Constitutive Equations From now on, we will assume that always exists an instantaneous elastic response.

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