John W. Hutchinson

Mixed mode cracking in layered materials

Publisher Summary This chapter describes the mixed mode cracking in layered materials. There is ample experimental evidence that cracks in brittle, isotropic, homogeneous materials propagate such that pure mode I conditions are maintained at the crack tip. An unloaded crack subsequently subject to a combination of modes I and II will initiate growth by kinking in such a direction that the advancing tip is in mode I. The chapter also elaborates some of the basic results on the characterization of crack tip fields and on the specification of interface toughness. The competition between crack advance within the interface and kinking out of the interface depends on the relative toughness of the interface to that of the adjoining material. The interface stress intensity factors play precisely the same role as their counterparts in elastic fracture mechanics for homogeneous, isotropic solids. When an interface between a bimaterial system is actually a very thin layer of a third phase, the details of the cracking morphology in the thin interface layer can also play a role in determining the mixed mode toughness. The elasticity solutions for cracks in multilayers are also elaborated.

STRAIN GRADIENT PLASTICITY: THEORY AND EXPERIMENT

Abstract Dislocation theory is used to invoke a strain gradient theory of rate independent plasticity. Hardening is assumed to result from the accumulation of both randomly stored and geometrically necessary dislocation. The density of the geometrically necessary dislocations scales with the gradient of plastic strain. A deformation theory of plasticity is introduced to represent in a phenomenological manner the relative roles of strain hardening and strain gradient hardening. The theory is a non-linear generalization of Cosserat couple stress theory. Tension and torsion experiments on thin copper wires confirm the presence of strain gradient hardening. The experiments are interpreted in the light of the new theory.

Singular behaviour at the end of a tensile crack in a hardening material.

Abstract D istributions of stress occurring at the tip of a crack in a tension field are presented for both plane stress and plane strain. A total deformation theory of plasticity, in conjunction with two hardening stress-strain relations, is used. For applied stress sufficiently low such that the plastic zone is very small relative to the crack length, the dominant singularity can be completely determined with the aid of a path-independent line integral recently given by rice (1967). The amplitude of the tensile stress singularity ahead of the crack is found to be larger in plane strain than in plane stress.

Metal Foams: A Design Guide

Introduction Making Metal Foams Characterization Methods Properties of Metal Foams Design Analysis for Material Selection Design Formulae for Simple Structures A Constitutive Model for Metal Foams Design for Creep with Metal Foams Sandwich Structures Energy Management: Packaging and Blast Protection Sound Absorption and Vibration Suppression Thermal Management and Heat Transfer Electrical Properties of Metal Foams Cutting, Finishing and Joining Cost Estimation and Viability Case Studies Suppliers of Metal Foams Web Sites Index .

Mechanisms controlling the durability of thermal barrier coatings

Abstract The durability of thermal barrier coatings is governed by a sequence of crack nucleation, propagation and coalescence events that accumulate prior to final failure by large scale buckling and spalling. Because of differing manufacturing approaches and operating scenarios, several specific mechanisms are involved. These mechanisms have begun to be understood. This article reviews this understanding and presents relationships between the durability, the governing material properties and the salient morphological features. The failure is ultimately connected to the large residual compression in the thermally grown oxide through its roles in amplifying imperfections near the interface. This amplification induces an energy release rate at cracks emanating from the imperfections that eventually buckle and spall the TBC.

Spontaneous formation of ordered structures in thin films of metals supported on an elastomeric polymer

Spontaneous generation of complex order in apparently simple systems is both arresting and potentially useful. Here we describe the appearance of complex, ordered structures induced by the buckling of thin metal films owing to thermal contraction of an underlying substrate. We deposit the films from the vapour phase on a thermally expanded polymer (polydimethylsiloxane, PDMS). Subsequent cooling of the polymer creates compressive stress in the metal film that is relieved by buckling with a uniform wavelength of 20–50 micrometres. The waves can be controlled and orientated by relief structures in the surface of the polymer, which can set up intricate, ordered patterns over large areas. We can account qualitatively for the size and form of the patterned features in terms of the non-uniform stresses developed in the film near steps on the polymer substrate. This patterning process may find applications in optical devices such as diffraction gratings and optical sensors, and as the basis for methods of strain analysis in materials.

THE RELATION BETWEEN CRACK GROWTH RESISTANCE AND FRACTURE PROCESS PARAMETERS IN ELASTIC-PLASTIC SOLIDS

CKA~K growth initiation and subsequent resistance is computed for an elastic-plastic solid with an idealized traction separation law specified on the crack plane to characterize the fracture process. The solid is specified by its Young’s modulus, E, Poisson’s ratio, v, initial tensile yield stress, (or, and strain hardening exponent, N. The primary parameters specifying the traction-separation law of the fracture process are the work of separation per unit area, To. and the peak traction, 6. Highly refined calculations have been carried out for resistance curves. K,(Arr), for plane strain, mode I growth in small-scale yielding as dependent on the parameters characterizing the elastic-plastic properties of the solid and its fracture process. With K,, = [El-,/( I ~ v’)] ’ 2 as the intensity needed to advance the crack in the absence ofplasticity, K,J& is presented in terms of its dependence on the two most important parameters, d/nr and N, with special emphasis on initiation toughness and steady-state toughness, Three applications of the results are made : to predict toughnesss when the fracture process is void growth and coalescence, to predict the role of plasticity on interface toughness for similar materials bonded together, and to illuminate the role of plasticity in enhancing toughness in dual-phase solids. The regime of applicability of the present model to ductile fracture due to void growth and coalescence, wherein multiple voids interact within the fracture process zone, is complementary to the regime of applicability of models describing the interaction between a single void and the crack tip. The two mechanism regimes are delineated and the consequence of a transition between them is discussed.

Mechanism-based strain gradient plasticity : I. Theory

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.

A phenomenological theory for strain gradient effects in plasticity

Abstract A Strain Gradient Theory of plasticity is introduced, based on the notion of statistically stored and geometrically necessary dislocations. The strain gradient theory fits within the general framework of couple stress theory and involves a single material length scale l. Minimum principles are developed for both deformation and flow theory versions of the theory which in the limit of vanishing l, reduce to their conventional counterparts: J2 deformation and J2 flow theory. The strain gradient theory is used to calculate the size effect associated with macroscopic strengthening due to a dilute concentration of bonded rigid particles; similarly, predictions are given for the effect of void size upon the macroscopibic softening due to a dilute concentration of voids. Constitutive potentials are derived for this purpose.

Bounds and Self-Consistent Estimates for Creep of Polycrystalline Materials

A study of steady creep of face centred cubic (f. c. c.) and ionic polycrystals as it relates to single crystal creep behaviour is made by using an upper bound technique and a self-consistent method. Creep on a crystallographic slip system is assumed to occur in proportion to the resolved shear stress to a power. For the identical systems of an f. c. c. crystal the slip-rate on any system is taken as γ = α(ז/ז0)n where α is a reference strain-rate, ז is the resolved shear stress and ז0 is the reference shear stress. The tensile behaviour of a polycrystal of randomly orientated single crystals can be expressed as ∊̄ = α(σ̄/σ̄0)n where ∊̄ are σ̄ the overall uniaxial strain-rate and stress and σ̄0 is the uniaxial reference stress. The central result for an f. c. c. polycrystal in tension can be expressed as σ̄0 = h(n) ז0. Calculated bounds to h(n) coincide at one extreme (n = ∞) with the Taylor result for rigid/perfectly plastic behaviour and at the other (n = 1) with the Voigt bound for linear viscoelastic behaviour. The self-consistent results, which are shown to be highly accurate for n = 1, agree closely with the upper bound for n ≽ 3. Two types of glide systems are considered for ionic crystals: A-systems, {110} <110>, with γ = α(ז/זA)n; and B-systems, {100} <110>, with γ = α(ז/זB)n. The upper bound to the tensile reference stress σ̄0 is shown to have the simple form σ̄0 ≼ A(n)זA+B(n)זB; A(n) and B(n) are computed for the entire range of n, including the limit n = ∞. Self-consistent predictions are again in good agreement with the bounds for high n. Upper bounds in pure shear are also calculated for both f. c. c. and ionic polycrystals. These results, together with those for tension, provide a basis for assessing the most commonly used stress creep potentials. The simplest potential based on the single effective stress invariant is found to give a reasonably accurate characterization of multiaxial stress dependence.