Local Plastic Failure Research Articles

Reduced stress propagation leads to increased mechanical failure resistance in auxetic materials

Materials with a negative Poisson ratio have the counterintuitive property of expanding laterally when they are stretched longitudinally. They are accordingly termed auxetic, from the Greek auxesis meaning to increase. Experimental studies have demonstrated auxetic materials to have superior material properties, compared with conventional ones. These include synclastic curvature, increased acoustic absorption, increased resilience to material fatigue, and increased resistance to mechanical failure. Until now, the latter observations have remained poorly understood theoretically. With this motivation, the contributions of this work are twofold. First, we elucidate analytically the way in which stress propagates spatially across a material following a localized plastic failure event, finding a significantly reduced stress propagation in auxetic materials compared with conventional ones. In this way, a plastic failure event occurring in one part of a material has a reduced tendency to trigger knock-on plastic events in neighboring regions. Second, via the numerical simulation of a lattice elastoplastic model, we demonstrate a key consequence of this reduced stress propagation to be an increased resistance to mechanical failure. This is seen not only via an increase in the externally measured yield strain, but also via a decreased tendency for plastic damage to percolate internally across a sample in catastrophic system-spanning clusters.

The (In)sensitivity of Granular Creep to Materials and Boundaries

AbstractSoils around the planet creep, despite wide variations in particle properties and environments. This sub‐yield “flow” of soil interacts with a variety of boundaries, in terms of geometry and friction. Here we explore the veracity of recent observations of undisturbed, gravity‐driven creep, by testing a suite of materials and boundary configurations in an experimental hillslope. Using an optical interferometry technique, we demonstrate that creep is a generic relaxation process whose qualitative dynamics are insensitive to grain properties. Velocity profiles are exponential, albeit with a defect near the no‐slip boundary. Quantitative patterns such as spatial variability and magnitude of strain rates, however, are exquisitely sensitive to the details of the experiment. The emerging picture is that creep is accomplished by localized plastic failure, which induces an elastic redistribution. Similar patterns have been observed in model glasses and on earthquake faults, indicating that sub‐yield relaxation in disordered materials may share common physics.

Localized forming limit analysis of substrate-supported metals: Influence of yield-dependent necking bound angle

In this paper, the influence of functional elastomeric substrate-supported layers for enhancing potential resistance capability against localized plastic failure of advanced high strength steels is considered based on a localized necking model of vertex theory. Application of this structure leads to postponing the plastic instability of the metallic part. By defining diffuse and localized modes of deformation in a general framework, the theoretical models are developed to predict necking limits at several stress states. In addition, the results of the Hookean and neo-Hookean elastomers are compared in terms of strain hardening with the anisotropy parameter of Hill’s yield criteria. Since necking band angle (NBA) is a principal factor for the necking prediction, its effect on bifurcation events is evaluated specifically for different ratios of stress rate, and quadratic and non-quadratic yield criteria. This analysis is performed by proposing a supported and yield-dependent necking bound angle (YD-NBA). All considerations are done by providing equilibrium conditions governed over the NBA. Finally, obtained results indicate good agreements between several theoretical considerations and experimental data.

Investigation of a Template‐Based Process Chain for Investment Casting of Open‐Cell Metal Foams

Herein, a holistic investigation of the process chain of polymer foam template manufacturing for the investment casting of open‐cell metal foams and their evaluation in terms of mechanical response under compressive loading is presented. Polymer foam templates are manufactured using sucrose beads as spaceholders with a body‐centred cubic (bcc) stacking and epoxy resin as matrix material. These templates are used in a modified investment casting process to produce commercial pure open‐cell Al foams (AA 1050 A). The materials used for the polymer foam templates are suitable for the template production and the use in investment casting. The structure of the template can be exactly reproduced by investment casting and no byproducts from the pyrolysis step can be detected within the molds or the Al foams. The mechanical properties under compressive loading are comparable with high‐strength Al‐alloy foams with a structure factor of C1 of 0.60. The characteristic plastic deformation is dominated by buckling, showing a local plastic failure of the struts within cell layers. Due to a high node‐to‐strut thickness ratio, neither small defects in the microstructure nor stacking errors of the template impact this deformation behavior.

Inferring the flow properties of epithelial tissues from their geometry

Amorphous materials exhibit complex material properties with strongly nonlinear behaviors. Below a yield stress they behave as plastic solids, while they start to yield above a critical stress Σc. A key quantity controlling plasticity which is, however, hard to measure is the density P(x) of weak spots, where x is the additional stress required for local plastic failure. In the thermodynamic limit P(x) ∼ x θ is singular at x = 0 in the solid phase below the yield stress Σc. This singularity is related to the presence of system spanning avalanches of plastic events. Here we address the question if the density of weak spots and the flow properties of a material can be determined from the geometry of an amorphous structure alone. We show that a vertex model for cell packings in tissues exhibits the phenomenology of plastic amorphous systems. As the yield stress is approached from above, the strain rate vanishes and the avalanches size S and their duration τ diverge. We then show that in general, in materials where the energy functional depends on topology, the value x is proportional to the length L of a bond that vanishes in a plastic event. For this class of models P(x) is therefore readily measurable from geometry alone. Applying this approach to a quantification of the cell packing geometry in the developing wing epithelium of the fruit fly, we find that in this tissue P(L) exhibits a power law with exponents similar to those found numerically for a vertex model in its solid phase. This suggests that this tissue exhibits plasticity and non-linear material properties that emerge from collective cell behaviors and that these material properties govern developmental processes. Our approach based on the relation between topology and energetics suggests a new route to outstanding questions associated with the yielding transition.

Three‐Dimensional Failure Patterns Around an Inflating Magmatic Chamber

AbstractBedrock failure around an inflating magma chamber is an important factor that controls the occurrence of volcanic eruptions. Here, we employ 3‐D numerical models of elasto‐plastic shear failure around an inflating crustal reservoir, to study how the induced failure patterns depend on the geometry of the chamber, on the host rock strength and on the gravitational field. Our simulations show that either localized or diffuse plastic failure domains develop in 3 stages. Failure initiates (stage 1) after a critical overpressure is reached, the value of which depends on effective host rock strength. Next, and with increasing applied overpressure, either distributed (for zero friction angle) or localized plastic failure zones (for 30 friction angle) form (stage 2), until they finally connect to the surface (stage 3). Cylindrical chambers develop prismatic shear zones that merge from the surface and chamber walls. For spherical and prolate chambers, diffuse conical zones of failure develop from the chamber's crest, whereas for oblate symmetrical chambers, shear bands initiate at the horizontal tips but bend back above the center of the chamber to reach the surface. In contrast for asymmetrical oblate chambers, shear bands initiate in their cylindrical section and vanish along the elongated direction. Here, magmatic fluids may migrate both through diffuse elastic dilation zones at the tips, and through localized shear zones from the crest. Our results thus suggest how natural observations may be used to constrain the mode of failure occurring underneath a volcano. We discuss several natural examples in this context.

Nonlinear instability problems including localized plastic failure and large deformations for extreme thermo-mechanical loads

In this work we provide the theoretical formulation, discrete approximation and solution algorithm for instability problems combing geometric instability at large displacements and material instability due to softening under combined thermo-mechanical extreme loads. While the proposed approach and its implementation are sufficiently general to apply to vast majority of structural mechanics models, more detailed developments are provided for truss-bar model. Several numerical simulations are presented in order to illustrate a very satisfying performance of the proposed methodology.

Analysis of the Stability of Ancient City Wall under Different Depths of Sapping by Numerical Calculation

The width of the top of the wall LIANGZHU ancient city , which is called the first city in China reaches 40-60m. The sapping depth made by around environment such as wind and sand is increasing years by years. So the problem of stability of wide top ancient wall has been put forward. Under different sapping depths in ancient city wall, using finite difference soft FLAC3D, We can build calculation model to study the failure laws and mechanism of the ancient city wall under different sapping depths. The research shows that when the sapping depth is not enough large, the whole city wall is stable and local plastic failure occurs around the sapping place. With the depth of sopping increasing, the plastic failure area is becoming bigger and bigger and reaches much deeper into the wall, even reaches the top of the wall, and the soil displacement becomes larger and larger until the whole wall sliding. The sapping contributes to the damage of the wall, the potential slide opening appears in the sapping area, and in the wall through plastic area appears, leading to the whole wall sliding.

Effects of material variability on the ductility of composite beams and overstrength coefficients

SUMMARYThe aim of this paper is to investigate the plastic rotation capacity of composite beams as well as the overstrength factors for composite joints considering the actual European steel production. It relies on the statistical data of the mechanical properties of steel profiles and reinforcement bars produced in several European steel mills that have been collected during the European research project OPUS. Several steel and composite structures have been designed following the EN 1998 rules, and the effect of the statistical distribution of the steel properties on the design has been analyzed. In such structures, the first attainment of the rotation capacity is expected to happen in the hogging region. The plastic rotation capacity was evaluated using the so‐called standard beam concept. The moment–rotation curve was constructed by joining together the pre‐buckling branch, determined using a fiber model, and the post‐buckling part derived by considering the local plastic failure mechanism as suggested by Gioncu. A program in MATLAB (MATLAB version 7.10.0. Natick, Massachusetts: The MathWorks Inc., 2010) was developed to establish such curve for arbitrary composite beams. The predictions of the model compare favorably against the experimental results. On the basis of the probabilistic model for the mechanical properties of steel, we derive the statistical distribution of the maximum rotation defined at the intersection of the pre‐buckling and post‐buckling curves. Next, we estimate the so‐called overstrength factors. Copyright © 2012 John Wiley & Sons, Ltd.

Dynamic plastic failure of a free–free slender tube under unsymmetrical linear distributed pressure

By employing theoretical analysis based on the rigid, perfectly plastic material idealization and finite element method based on elastic, perfectly plastic material idealization, a comprehensive analysis of dynamic behavior of a free–free tube beam under arbitrary unsymmetrical linear distributed pressure has been made in this paper. Because the distribution of the load is more general, the theoretical result can be degenerated into some special cases which had been discussed in [1,2]. The comparisons between results of present theoretical analysis and those obtained from finite element calculation show that there is a dangerous region between the center of the tube beam and the pressure peak position, in which the local plastic collapse may take place. The theoretical results can provide a simple approximate estimation of local plastic failure position and deformation profile of aerospace vehicles subjected to the pressure pulse resulting from an explosion.

Development of a Three-dimensional Model for Ductile Fracture in Materials Containing Two Types of Microvoids.

There are three stages in ductile fracture process: voids initiation, void growth and void coalescence. In the final stage, ductile fracture occurs due to the void coalescence. Thomason suggested that voids begin to coalesce when a plastic limit-load condition is fulfilled for localized plastic failure of the intervoid matrix. On the basis of this critical void-coalescence condition, we developed a three-dimensional model for ductile fracture considering two types of voids with different sizes, and applied this model to a SA440 steel with and without pre-straining. With the critical strength of particle/matrix interface and the theoretical void growth strain obtained from the model, the reason for the decrease in fracture strain caused by plastic pre-strain was discussed.

Toughness and microscopic fracture mechanisms of unfilled and short-glass-fibre-filled poly(cyano arylether)

Fracture mechanisms of an advanced high-strength thermoplastic poly(cyano arylether) (PCAE) and its short-glass-fibre (SGF)-reinforced composites have been studied in relation to toughnesses K c and J c. Test temperatures were 23 and 100 °C. Reflected and transmitted optical observations were combined with scanning electron microscopy for the fractographic investigation. For unreinforced PCAE tested at 100 °C, the damage area in front of a notch becomes fairly large in size and consists of numerous tensile microfailures around the local plastic yielding zone, as compared with that tested at 23 °C. This resulted in a substantial improvement of K c and a big increase in J c. Filling fibres, however, produced both toughening and anti-toughening results: effects of fibre spanning, pull-out and bridging across the local plastic failure zone and zigzag propagation of fracture due to fibre filling, improved the toughness. However, adhesive failure at the fibre-matrix interface, tensile microcleavage at the fibre ends and straightforward fracture in the skin layer, considerably diminished the values of K c and J c, except for the trend of K c at 23 °C.

Local plastic failure of light gauge steel roofing sheets: Finite element analysis versus experiment

Abstract Screw-fastened light gauge steel profiled roof sheeting, which is widely used in houses and other low-rise buildings, may fail locally in the vicinity of the screw fastener by plastic collapse under strong peak wind loads or by cracking due to low cycle fatigue under sustained fluctuating wind loads, resulting in the sheeting being pulled over the fastener. Loss of roofing sheets can then lead to overloading of other structural elements, with the consequence often being the collapse of the entire building. Several experimental studies have been carried out on the local plastic failure and fatigue strength of roofing sheets, but the problem has been subjected to only limited rigorous theoretical analysis. This paper therefore presents a study on the finite element modelling of the collapse behaviour of trapezoidal profile sheeting under monotonic loads. Elastic-plastic large deflection finite element analyses using the Semi-Loof shell element are carried out and the results compared with those from carefully conducted experiments. The close agreement between the finite element and test results validates the finite element model. The success of the finite element model opens the way for theoretical modelling of the failure behaviour of roofing sheets, the optimal design of sheeting profiles, and for future work on cyclone-induced fatigue of roofing sheets which requires a detailed examination of stresses and strains in the vicinity of fastener holes.