Effect of creep prestrain on subsequent plastic deformation

The effect of creep prestrain on subsequent plastic deformation is experimentally investigated. The experiments are performed by subjecting thin-walled tubular specimens of stainless steel SUS 304 after creep prestraining to combined axial load and torsion at room temperature to 600°C. The stress-strain relations subsequent to creep prestrain are determined under combined stress state with and without temperature changes in prestraining and subsequent plastic straining. On the experimental results, the plastic hardening effects by creep prestrain are discussed under various temperature conditions. The subsequent stress-strain relations are compared with the calculated results on the equi-plastic strain surfaces.     

Shakedown theory for elastic plastic kinematic hardening bodies

Shakedown static and kinematic theorems for elastic–plastic (generally nonlinear) kinematic hardening solids are derived in classical (path-independence) spirit with new constructions. The generally plastic-deformation-history-dependent hardening curve is assumed to be limited by the initial yield stress and ultimate yield strength, and to obey a positive hysteresis postulate for closed plastic cycles, but else can be arbitrary and unspecified. The theorems reveal that the shakedown of structures is not affected by the particular form of the hardening curve, but just by the initial and ultimate yield stresses. While the ultimate yield strength is clearly defined macroscopically and attached to the incremental collapse mode with unbounded plastic deformations, the initial yield stress, which is responsible for the bounded cyclic plasticity collapse mode, should not be taken as the convenient one at a fixed amount of plastic deformation (0.2%), but is suggested to be taken as low as the fatigue limit to preserve the classical load-history-independence spirit of the shakedown theorems. Otherwise, for our pragmatic application purpose, it may be given empirical values between the low fatigue limit and high ultimate yield stresses according to particular loading processes considered, which may range anywhere between the high-cycle and low-cycle ones. The theorems appear as simple as those of Melan and Koiter for perfect plasticity but applied to the much larger class of more realistic kinematic hardening materials.     

Orientational anisotropy for Rouse eigenmodes during creep and recovery process

The Rouse model is a well established model for nonentangled polymer chains and its dynamic behavior under step strain has been fully analyzed in the literature. However, to the knowledge of the authors, no analysis has been made for the orientational anisotropy for the Rouse eigenmodes during the creep and creep recovery processes. For completeness of the analysis of the Rouse model, this anisotropy is calculated from the Rouse equation of motion. The calculation is simple and straightforward, but the result is intriguing in a sense that respective Rouse eigenmodes do not exhibit the single Voigt-type retardation. Instead, each Rouse eigenmode has a distribution in the retardation time. This behavior, reflecting the interplay among the Rouse eigenmodes of different orders under the constant stress condition, is quite different from the behavior under rate-controlled flow (where each eigenmode exhibits retardation/relaxation associated with a single characteristic time).List of abbreviations and symbols a Average segment size at equilibrium - A_p(t) Normalized orientational anisotropy for the p-th Rouse eigenmode defined by Eq. (14) - p-th Fourier component of the Brownian force (=x, y) - F_B(n,t) Brownian force acting on n-th segment at time t - G(t) Relaxation modulus - J(t) Creep compliance - J_R(t) Recoverable creep compliance - k_B Boltzmann constant - N Segment number per Rouse chain - Q_j(t) Orientational anisotropy of chain sections defined by Eq. (21) - r(n,t) Position of n-th segment of the chain at time t - S(n,t) Shear orientation function (S(n,t)=a^–2<u_x(n,t)u_y(n,t)>) - T Absolute temperature - u(n,t) Tangential vector of n-th segment at time t (u = r/n) - V(r(n,t)) Flow velocity of the frictional medium at the position r(n,t) - X_p(t), Y_p(t), and Z_p(t) x-, y-, and z-components of the amplitudes of p-th Rouse eigenmode at time t - Strain rate being uniform throughout the system - Segmental friction coefficient - ₀ Zero-shear viscosity - _p Numerical coefficients determined from Eq. (25) - Gaussian spring constant ( = 3k_BT/a²) - Number of Rouse chains per unit volume - (t) Shear stress of the system at time t - _steady Shear stress in the steadily flowing state - _R Longest viscoelastic relaxation time of the Rouse chain     

Model of plastic anisotropy evolution with texture-dependent yield surface

Model of evolution of plastic anisotropy due to crystallographic texture development, in metals subjected to large deformation processes, is presented. The model of single grain with the regularized Schmid law proposed by Gambin is used. Evolution of crystallographic texture during drawing, rolling and pure shear is calculated. Phenomenological texture-dependent yield surface for polycrystalline sheets is proposed. Evolution of this yield surface is compared with evolution of phenomenological higher order yield surfaces proposed by Hill and Barlat with Lian for drawing, rolling and pure shear processes. The change of the Hill yield surface and the Barlat–Lian yield surface is obtained by replacing material parameters present in these conditions by texture-dependent functions.     

A gradient theory of small-deformation isotropic plasticity that accounts for the Burgers vector and for dissipation due to plastic spin

This study develops a gradient theory of small-deformation viscoplasticity based on: a system of microforces consistent with its peculiar balance; a mechanical version of the second law that includes, via the microforces, work performed during viscoplastic flow; a constitutive theory that accounts for the Burgers vector through a free energy dependent on , with H^p the plastic part of the elastic-plastic decomposition of the displacement gradient. The microforce balance and the constitutive equations, restricted by the second law, are shown to be together equivalent to a nonlocal flow rule in the form of a coupled pair of second-order partial differential equations. The first of these is an equation for the plastic strain-rate in which the stress T plays a basic role; the second, which is independent of T, is an equation for the plastic spin. A consequence of this second equation is that the plastic spin vanishes identically when the free energy is independent of, but not generally otherwise. A formal discussion based on experience with other gradient theories suggests that sufficiently far from boundaries solutions should not differ appreciably from classical solutions, but close to microscopically hard boundaries, boundary layers characterized by a large Burgers vector and large plastic spin should form.Because of the nonlocal nature of the flow rule, the classical macroscopic boundary conditions need be supplemented by nonstandard boundary conditions associated with viscoplastic flow. As an aid to solution, a variational formulation of the flow rule is derived.Finally, we sketch a generalization of the theory that allows for isotropic hardening resulting from dissipative constitutive dependences on .     

Relations of the theory of translational perfectly plastic anisotropy in the case of plane deformation

Relations of the theory of translational anisotropy in the case of plane deformation are considered. Some properties of solutions of the original equations are established. The equations for characteristics and some relations along the characteristics are determined.     

Estimating the plastic strain with the use of acoustic anisotropy

Experimental verification is used to show that reference specimens and structure unloading do not permit obtaining an adequate estimate of plastic strain by measuring the acoustic anisotropy. Analytic estimates of the speed of propagation of a plane acoustic wave of various polarizations in an elastoplastic material in the direction orthogonal to the action of preliminary uniaxial stress are obtained. An analysis of the obtained relations reveala an advantage of using absolute values of the velocity of longitudinal and transverse waves for the plastic strain identification. In contrast to acoustic anisotropy, the velocities vary monotonically in a wider range of plastic strains. At the same time, the elastic strain does not affect the longitude wave velocity, which allows one to use the measurement results to estimate the character of strains.     

Assessment of creep crack growth due to stress relief

An analysis is conducted to predict stress relief cracking at 550 °C in notched compact tension specimens of Type 316H austenitic stainless steel. The specimens had been subjected to pre-compression to generate a tensile residual stress distribution at the notch tip. This stress distribution is represented by a uniform reference stress over the zone of tension ahead of the notch tip. Creep rupture and creep crack growth data alone are required and used to make the predictions. It is found that the shape of the crack growth curve is correctly predicted when mean data are employed. However, upper bound crack growth properties are required to accurately predict the actual extent of cracking. Sensitivity studies show that the amount of stress relief cracking predicted is relatively insensitive to the reference stress initially assumed to describe the residual stress distribution, since the reference stress relaxes to a magnitude that is almost independent of its initial value. Adoption of an initial reference stress equal to the ultimate tensile strength of the steel, when combined with mean creep rupture and upper bound crack growth properties, results in safe predictions that are not overly conservative. The analysis should only be regarded as reliable for small amounts of crack extension of less than the size of the tensile zone ahead of the crack tip.     

Unit cell debonding analyses for arbitrary orientation of plastic anisotropy

Debonding of rigid inclusions embedded in the elastic–plastic aluminum alloy Al 2090-T3 is analyzed numerically using a unit cell model taking full account of finite strains. The cell is subjected to overall biaxial plane strain tension and periodical boundary conditions are applied to represent arbitrary orientations of plastic anisotropy. Plastic anisotropy is considered using two phenomenological anisotropic yield criteria, namely Hill [Proceedings of the Royal Society of London A 193 (1948) 281] and Barlat et al. [International Journal of Plasticity 7 (1991) 693]. For this material plastic anisotropy delays debonding compared to plastic isotropy except for the case of Hill’s yield function when the tensile directions coincided with the principal axes of anisotropy. For some inclinations of the principal axes of anisotropy relative to the tensile directions, the stress strain responses are identical but the deformation modes are mirror images of each other.     

On plastic anisotropy of constitutive model for rate-dependent single crystal

An algorithm for single crystals was developed and implemented to simulate plastic anisotropy using a rate-dependent slip model. The proposed procedure was a slightly modified form of single crystal constitutive model of Sarma and Zacharia. Modified Euler method, together with Newton-Raphson method was used to integrate this equation which was stable and efficient. The model together with the developed algorithm was used to study three problems. First, plastic anisotropy was examined by simulating the crystal deformation in tension and plane strain compression, respectively. Secondly, the orientation effect of some material parameters in the model and applied strain rate on plastic anisotropy for single crystal also is investigated. Thirdly, the influence of loading direction on the active slip system was discussed.     

Permeability anisotropy due to consolidation of compressible porous media

The characterisation of flow through porous media is important for all solid–liquid separation and fluid transport realms. The permeability of porous media can be anisotropic and furthermore, the extent of anisotropy can be increased as a result of an applied compressive force. However, the understanding of how anisotropy develops is incomplete. An overview of research on permeability anisotropy is given and an expression for predicting anisotropy as a function of void ratio is offered. The two underlying assumptions of the proposed model are: flow in different directions occurs within the same network of pores and deformation is primarily due to the compression of the particles in the direction of the applied force rather than due to particle rearrangement. The assumption of network connectivity allows permeability anisotropy to be described as a function of flow path tortuosity only. Results are presented for hydraulic anisotropy measured in lignite that has been upgraded by a compression dewatering method known as mechanical thermal expression. The lignite permeability is shown to be up to eight times greater in the direction perpendicular to compression, suggesting that the rate of dewatering could be significantly increased by choosing the drainage to also be perpendicular to the direction of the applied compressive force. It is illustrated that the proposed anisotropy model can be used to accurately predict the experimentally determined permeability anisotropy ratios for lignite, as well as for other materials including sand, clay and kaolin.     

Mechanics of nonbuckling interconnects with prestrain for stretchable electronics

The performance of the flexibility and stretchability of flexible electronics depends on the mechanical structure design, for which a great progress has been made in past years. The use of prestrain in the substrate, causing the compression of the transferred interconnects, can provide high elastic stretchability. Recently, the nonbuckling interconnects have been designed, where thick bar replaces thin ribbon layout to yield scissor-like in-plane deformation instead of in-or out-of-plane buckling modes. The nonbuckling interconnect design achieves significantly enhanced stretchability. However,combined use of prestrain and nonbuckling interconnects has not been explored. This paper aims to study the mechanical behavior of nonbuckling interconnects bonded to the prestrained substrate analytically and numerically. It is found that larger prestrain,longer straight segment, and smaller arc radius yield smaller strain in the interconnects.On the other hand, larger prestrain can also cause larger strain in the interconnects after releasing the prestrain. Therefore, the optimization of the prestrain needs to be found to achieve favorable stretchability.     

A simple law of steady-state creep for material with anistropy introduced by plastic prestraining

Summary The Odqvist theory is generalized by employing a plastic prestrain-induced anisotropy tensor of rank four, which is a linear combination of fourth rank tensors formed by the isotropic tensor _ij and the prestrain effect tensor e( _ij ^p .The constitutive equation is verified by uniaxial creep experiments carried out on thin-walled tubular specimens of pure copper deformed previously at room temperature under combined tension and torsion stresses.

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Ein einfaches Gesetz für stationäres Kriechen von Werkstoffen mit Anisotropie infolge plastischer Vorverformung

Übersicht Die von Odqvist aufgestellte Theorie wird durch die Verwendung eines Tensors vierter Stufe, der die Anisotropie infolge plastischer Verformung beschreibt, verallgemeinert. Der benutzte Tensor stellt eine Linearkombination von Tensoren vierter Stufe dar, die aus dem isotropen Tensor _ij und dem Vorverformungstensor e( _ij ^p gebildet werden.Das Stoffgesetz wird an einachsigen Kriechversuchen mit dünnwandigen Rohrproben aus reinem Kupfer überprüft, die zuvor bei Raumtemperatur durch eine kombinierte Zug- und Torsionsspannung verformt worden sind.

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This paper was presented at the Third Symposium on Mechanics of Inelastic Solids and Structures held in Bad Honnef in September 1984

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The author wishes to dedicate this paper to the memory of Prof. A. Sawczuk     

An endochronic theory accounted for deformation induced anisotropy

An anisotropic quadratic form of plastic strain increment is used to define the intrinsic time in the endochronic theory of plasticity. Based on this new definition, a yield function can be derived. This new version of endochronic theory can describe the expansion, translation, rotation, and distortion of the yield surface. While the initial yielding is in the form of the Mises yield criterion, the distortion of subsequent yield surfaces is expressed by the compression or stretching of the Mises yield surface. The effect of sharp front and blunt rear of the yield surface is considered to be of secondary importance and neglected in the interest of keeping the equations simple. This idealization will not much affect the prediction power of the model, because the plastic strain increment is in the radial direction emanating from the center of the current yield surface and is not normal to the current yield surface. In this theory, the plastic deformation is thus not sensitive to the exact shape of the yield surface. It has been shown that the proposed theory is capable of describing the experimental results of three different metals considered. The test series investigated include several different paths of prestress.