Person:

Hutchinson, John

The failure process ahead of a mode I crack advancing in a ductile thin metal plate or sheet produces plastic dissipation through a sequence of deformation steps that include necking well ahead of the crack tip and shear localization followed by a slant fracture in the necked region somewhat closer to the tip. The objective of this paper is to analyze this sequential process to characterize the traction–separation behavior and the associated effective cohesive fracture energy of the entire failure process. The emphasis is on what is often described as plane stress behavior taking place after the crack tip has advanced a distance of one or two plate thicknesses. Traction–separation laws are an essential component of finite element methods currently under development for analyzing fracture of large scale plate or shell structures. The present study resolves the sequence of failure details using the Gurson constitutive law based on the micromechanics of the ductile fracture process, including a recent extension that accounts for damage growth in shear. The fracture process in front of an advancing crack, subject to overall mode I loading, is approximated by a 2D plane strain finite element model, which allows for an intensive study of the parameters influencing local necking, shear localization and the final slant failure. The deformation history relevant to a cohesive zone for a large scale model is identified and the traction–separation relation is determined, including the dissipated energy. For ductile structural materials, the dissipation generated during necking prior to the onset of shear localization is the dominant contribution; it scales with the plate thickness and is mesh-independent in the present numerical model. The energy associated with the shear localization and fracture is secondary; it scales with the width of the shear band, and inherits the finite element mesh dependency of the Gurson model. The cohesive traction–separation laws have been characterized for various material conditions.

Nanopores fabricated in free-standing amorphous silicon thin films were observed to close under 3 keV argon ion irradiation. The closing rate, measured in situ, exhibited a memory effect: at the same instantaneous radius, pores that started larger close more slowly. An ion-stimulated viscous flow model is developed and solved in both a simple analytical approximation for the small-deformation limit and in a finite element solution for large deformations. The finite-element solution exhibits surprising changes in cross-section morphology, which may be extremely valuable for single biomolecule detection, and are untested experimentally. The finite-element solution reproduces the shape of the measured nanopore radius versus fluence behavior and the sign and magnitude of the measured memory effect. We discuss aspects of the experimental data not reproduced by the model, and successes and failures of the competing adatom diffusion model.

Small scale explosive loading of sandwich panels with low relative density pyramidal lattice cores has been used to study the large scale bending and fracture response of a model sandwich panel system in which the core has little stretch resistance. The panels were made from a ductile stainless steel and the practical consequence of reducing the sandwich panel face sheet thickness to induce a recently predicted beneficial fluid–structure interaction (FSI) effect was investigated. The panel responses are compared to those of monolithic solid plates of equivalent areal density. The impulse imparted to the panels was varied from 1.5 to 7.6 kPa s by changing the standoff distance between the center of a spherical explosive charge and the front face of the panels. A decoupled finite element model has been used to computationally investigate the dynamic response of the panels. It predicts panel deformations well and is used to identify the deformation time sequence and the face sheet and core failure mechanisms. The study shows that efforts to use thin face sheets to exploit FSI benefits are constrained by dynamic fracture of the front face and that this failure mode is in part a consequence of the high strength of the inertially stabilized trusses. Even though the pyramidal lattice core offers little in-plane stretch resistance, and the FSI effect is negligible during loading by air, the sandwich panels are found to suffer slightly smaller back face deflections and transmit smaller vertical component forces to the supports compared to equivalent monolithic plates.

Wrinkling of thin stiff films on thick compliant elastomeric substrates subject to plane strain compression is considered for cases in which the substrate is pre-stretched prior to film attachment. Advanced wrinkling modes are investigated that evolve as the systems are compressed beyond the onset of the primary sinusoidal wrinkling mode. If the substrate pre-stretch is greater than about 40%, an advanced mode in the form of a series of well-spaced ridges separated by relatively flat film is observed in the simulations. Our experiments reveal a localization mode in the form of alternating packets of large and small amplitude wrinkles, but not ridges, while ridge formation has been observed in other recent experiments. Measurements of undulation amplitudes have been made for wrinkle fields of stiff films formed by oxidation of the surface of pre-stretched PDMS substrates. Simulations have been performed with a finite element model and an analytical film/substrate model. The formation of the ridge mode is a consequence of the altered nonlinearity of the substrate produced by the pre-stretch. The role of the tangential substrate stiffness in suppressing localization at the ridges is also highlighted. If there is no substrate pre-stretch, or if the substrate is pre-compressed, the primary sinusoidal mode gives way to an entirely different sequence of advanced modes usually entailing period doubling followed by folding. The nature of substrate nonlinearity that leads to ridges or folds is discussed.

Thin stiff films on compliant elastic substrates subject to equi-biaxial compressive stress states are observed to buckle into various periodic mode patterns including checkerboard, hexagonal and herringbone. An experimental setting in which these modes are observed and evolve is described. The modes are characterized and ranked by the extent to which they reduce the elastic energy of the film–substrate system relative to that of the unbuckled state over a wide range of overstress. A new mode is identified and analyzed having nodal lines coincident with an equilateral triangular pattern. Two methods are employed to ascertain the energy in the buckled state: an analytical upper-bound method and a full numerical analysis. The upper-bound is shown to be reasonably accurate to large levels of overstress. For flat films, except at small states of overstress where the checkerboard is preferred, the herringbone mode has the lowest energy, followed by the checkerboard, with the hexagonal, triangular, and one-dimensional modes lowering the energy the least. At low overstress, the hexagonal mode is observed in the experiments not the square mode. It is proposed that a slight initial curvature of the film may play role in selecting the hexagonal pattern accompanied by a detailed analysis. An intriguing finding is that the hexagonal and triangular modes have the same energy in the buckled state and, moreover, a continuous transition between these modes exists involving a linear combination of the two modes with no change in energy. Experimental observations of various periodic modes are discussed with reference to the energy landscape. Discrepancies between observations and theory are identified and open issues are highlighted.

A systematic study of factors affecting the delamination energy release rate and mode mix of a thermal barrier coating attached to a substrate is presented accounting for the influence of thermal gradients combined with rapid hot surface cooling. Transient thermal gradients induce stress gradients through the coating and substrate, which produce overall bending if the substrate is not very thick and if it is not constrained. Due to their influences on the coating stresses, substrate thickness and constraint are important aspects of the mechanics of delamination of coating-substrate systems, which must be considered when laboratory tests are designed and for lifetime assessment under in-service conditions. Temperature gradients in the hot state combined with rapid cooling give rise to a maximum energy release rate for delamination that occurs in the early stage of cooling and that can be considerably larger than the driving force for delamination in the cold state. The rates of cooling that give rise to a large early stage energy release rate are identified.

The stability of the wrinkling mode experienced by a compressed half-space of neo-Hookean material is investigated using analytical and numerical methods to study the post-bifurcation behaviour of periodic solutions. It is shown that wrinkling is highly unstable owing to the nonlinear interaction among the multiple modes associated with the critical compressive state. Concomitantly, wrinkling is sensitive to exceedingly small initial imperfections that significantly reduce the compressive strain at which the instability occurs. The study provides insight into the connection between wrinkling and an alternative surface mode, the finite amplitude crease or sulcus. The shape of the critical combination of wrinkling modes has the form of an incipient crease, and a tiny initial imperfection can trigger a wrinkling instability that collapses into a crease.

Wrinkling modes are determined for a two-layer system comprised of a neo-Hookean film bonded to an infinitely deep neo-Hookean substrate with the entire bilayer undergoing compression. The full range of the film/substrate modulus ratio is considered from the limit of a traction-free homogeneous substrate to very stiff films on compliant substrates. The role of substrate prestretch is considered wherein an unstretched film is bonded to a prestretched substrate with wrinkling arising as the stretch in the substrate is relaxed. An exact bifurcation analysis reveals the critical strain in the film at the onset of wrinkling. Numerical simulations carried out within a finite element framework uncover advanced post-bifurcation modes including period-doubling, folding and a newly identified mountain ridge mode.

Cropping is a cutting process whereby opposing aligned blades create a shearing failure by exerting opposing forces normal to the surfaces of a metal sheet or plate. Building on recent efforts to quantify cropping, this paper formulates a plane strain elastic-plastic model of a plate subject to shearing action by opposing rigid platens. Shear failure at the local level is modeled by a cohesive zone characterized by the peak shear traction and the energy dissipated by shear failure process at the microscopic level. The model reveals the interplay between shear cracking and the extensive plastic shearing accompanying the cutting process. Specifically, it provides insight into the influence of the material’s microscopic shear strength and toughness on the total work of cropping. The computational model does not account for deformation of the cropping tool, friction between sliding surfaces and material temperature and rate-dependence.

Experiments on soft polycrystalline aluminum have yielded evidence that, besides the required punch load, both the size and shape of imprinted features are affected by the scale of the set-up, e.g. substantial details are lost when the characteristic length is on the order of 10µm. The objective of this work is to clarify the role played by strain gradients on this issue, and to shed light on the underlying mechanisms. For this, indentation by a periodic array of flat punch indenters is considered, and a gradient enhanced material model that allows for a numerical investigation of the fundamentals are employed. During a largely non-homogeneous deformation, the material is forced up in between the indenters so that an array of identical imprinted features is formed once the tool is retreated. It is confirmed that the additional hardening owing to plastic strain gradients severely affects both the size and shape of these imprinted features. In particular, this is tied to a large increase in the mean contact pressure underneath the punch, which gives rise to significant elastic spring-back effects during unloading.