A V-notched bar pulled in tension in plane strain as shown in Fig. 1 is considered. The distribution of stress and deformation are determined from the analysis of the motion with large strains as the initial notch width pulls down toward line contact as the test proceeds. The analysis is based upon the theory of flow of a so-called Saint Venant-Mises material, which flows at a constant yield limit given by the Mises criterion, and obeys the Mises flow-type relationship between stress and strain increments. The successive configurations of an initially square grid on the cross section of the notch are obtained to illustrate the strain distribution. This solution is of interest in investigating the initiation of fracture in a notch-bar tension test. In such a test the foregoing type of solution applies until plastic flow is arrested by the appearance of a fracture crack. The variation of the solution with notch angle is of interest in connection with the determination of the technical cohesive strength of a metal using Kuntze’s technique. The present solution indicates a contrast with Kuntze’s hypothesis, in that it predicts the possibility of a plastic-flow type of rupture at a stress depending only upon the yield stress of the metal.

An analysis of longitudinal impact tests that were made by Drs. D. S. Clark and P. E. Duwez at the California Institute of Technology on an iron and a steel with definite yield points is described. From this analysis is deduced the probable nature of the dynamic stress-strain relations for such materials. These appear to differ greatly from the static stress-strain relations, unlike the case for materials without yield points. As pointed out by Duwez and Clark, the upper yield stress for undeformed material is several times as great under impact as the static yield stress. The present analysis indicates that under impact, the material with a definite yield point is made harder at a given deformation, and ruptures at a higher (engineering) stress and smaller strain than when loaded statically. The critical impact velocity, defined as that at which nearly instantaneous failure occurs in tension, is discussed, and the factors upon which it depends are given.

Combined-stress tests were made on five 24S-T aluminum-alloy tubes, 1 3/4 in. ID × 0.05 in. thick. The ratios of circumferential (hoop) stress to axial stress were 0, 1/2, 1, 2, and ∞. The tubes were tested to failure and sufficient measurements of circumferential strain and axial strain were taken to plot stress-strain curves almost up to rupture. The results are presented in the form of two sets of stress-strain curves for each ratio of stresses, namely, maximum shearing stress plotted against maximum shearing strain, and octahedral shearing stress plotted against octahedral shearing strain. In each plot the maximum deviation of the curves is about ± 5 per cent. A method of evaluating small octahedral shearing strains from the data is given which does not assume Poisson’s ratio to be 1/2.

A method is presented for predicting the final strained state of a long uniform bar or wire of ductile material that is subjected to a longitudinal impact of finite duration during which the impact stress is constant and exceeds the yield strength. It is shown that for a long specimen this corresponds to giving the point of impact a constant velocity during the impact interval. (After this interval the stress at the end of the member is zero, but not its particle velocity.) It is also shown that the final unit strains are greatest immediately adjacent to the impact point and are constant over a finite length of specimen. Following this region of constant residual strain is a region, also of finite length, in which the permanent strain decreases steadily with distance from the end of the specimen. At the end of this there is another zone of constant permanent strain, which is followed by one of decreasing permanent strain, and so on. It is shown that there is a definite relation between the stress history at a point of a specimen and the velocity of that point—this relation is given. It is demonstrated that in tensile impact a critical velocity of impact can be defined, corresponding to the ultimate strength of the material. At impact velocities greater than this critical velocity, rupture occurs quickly and close to the point of impact so that the remainder of the specimen does not receive large deformations. Thus the energy required to break a specimen in tension is less at supercritical than at subcritical impact velocities.

Results of combined stress tests on a medium-carbon steel are presented. Particular attention has been paid to the magnitude and the distribution of the stresses and strains at the instant preceding fracture. The effect of the shape of the test specimen and the isotropy of the material upon the rupture properties have also been investigated. This investigation was carried out at the Westinghouse Research Laboratories under a contract with the David Taylor Model Basin, Bureau of Ships, U. S. Navy Department, according to plans worked out by Captain W. P. Roop, U.S.N., of the David Taylor Model Basin, and Dr. A. Nadai of Westinghouse.

Motivated by recent, unexpected, experimental observations of “intersonic” rupture growth in which both shear and dilatational Mach fronts were observed at the tips of dynamic frictional ruptures propagating at rupture speeds below the dilatational wave speed of the surrounding solid, and we formulate the general dynamic flexoelectric problem and we investigate its plane strain/plane polarization specialization. The coupling of the mechanical problem is analogous to a problem of Toupin–Mindlin gradient elasticity, where two micromechanical characteristic lengths and two microinertial lengths emerge as a combination of the mechanical, dielectric, and flexoelectric constants. The solution of the rupture growth problem allows us to provide an explanation of the experimental results. This becomes possible since flexoelectricity predicts a new aspect that was not observed in the classical analysis: subsonic super shear and supersonic crack tip (or rupture) motions are not related exclusively with the problem being elliptic or hyperbolic, respectively. This is due to the influence of the microinertial lengths, which, in addition to the ratios of the rupture to the wave speeds, also affect the slopes of the Mach cones. Moreover, we are able to explain the experimental paradox of the observation of double Mach cone pairs at the tips of supershear, but subsonic, frictional, ruptures in poly-methyl-methacrtylate (PMMA) by demonstrating that both dilatational and shear Mach cones could appear in flexoelectric solids at rupture speeds below the material dilatation wave speed, something that is impossible from the classical elasticity analysis and is due to the dispersive nature of the present problem. Our analysis is of relevance to the dynamic deformation and fracture of both synthetic and naturally occurring flexoelectric materials and systems, with implications to both engineering and earthquake source mechanics.

Scar structures of natural animals can reinforce the wounds both mechanically and biologically to maintain the functions of the injured muscle and skin. Inspired by the scar structure, we present a dielectric elastomer (DE) with silver nanowire electrodes possessing the scar-like ability. This DE membrane can tolerate the failures by both electric breakdown and mechanical rupture. The DE actuator (DEA) can maintain their performances of force and displacement output after multiple failures. Scanning electronic microscope (SEM) images show that the scar-like structures accumulate around the electromechanical failure locations on the DE membrane as the stiffened and insulated regions, which prevent further short current and membrane rupture. J-integrals and stress distribution around the failure location have been calculated by finite element analysis to verify the mechanical reinforcements of the scar-like structures over crack propagation.

The immobilization of receptor–ligand molecules in dynamic force spectroscopy (DFS) often relies on an extra noncovalent linkage to solid surfaces, resulting in two barrier-crossing diffusion processes in series and concurrent bond dissociations. One outstanding theoretical issue is whether the linkage between the immobilizer and biomolecule is sufficiently strong during repeated force ramping in the measurements and how it might influence the interpretation on receptor–ligand kinetics. Following the classical framework by Kramers, we regard each dissociation process as a flux of probabilistic bond configuration outward over an energy barrier in the coordinated energy landscape, and solve the two coupled boundary value problems in the form of Smoluchowski equation. Strong kinetic and mechanical coupling is observed between the two molecular bonds in series, with the results showing that involving a noncovalent linkage in DFS can obscure the unbinding characteristics of the receptor–ligand bond. Our approach provides a quantitative assessment to the hidden effects of having a fragile molecular anchorage in DFS and allows the corrected interpretation on receptor–ligand dissociation kinetics in the case.

Optimization of material microstructure is strongly tied with the performance of composite materials at the macroscale and can be used to control desired macroscopic properties. In this paper, we study the optimal location of carbon black (CB) particle inclusions in a natural rubber (NR) matrix with the objective to maximize the rupture resistance of such polymer composites. Hyperelasticity is used to model the rubber matrix and stiff inclusions, and the phase field method is used to model the fracture accounting for large deformation kinematics. A genetic algorithm is employed to solve the inverse problem in which three parameters are proposed as optimization objective, including maximum peak force, maximum deformation at failure-point, and maximum fracture energy at failure-point. Two kinds of optimization variables, continuous and discrete variables, are adopted to describe the location of particles, and several numerical examples are carried out to provide insight into the optimal locations for different objectives.

Existing experimental and theoretical studies on the adhesion of molecular bond clusters are usually based on either displacement- or force-controlled loading conditions. Very few studies have addressed whether or not and how the loading conditions affect the stochastic behavior of clusters. By considering the reversible breaking and rebinding process of ligand–receptor bonds, we directly solve the master equation about reactions between receptor–ligand bonds and conduct the corresponding Monte Carlo simulation to investigate the rupture forces of adhesion molecular clusters under linearly incremented displacement and force loading, respectively. We find that the rupture force of clusters strongly depends on loading conditions. Bond breaking and rebinding are independent of each other under displacement-controlled loading, whereas the rupture force highly depends on the state of each single bond under force-controlled loading. The physical mechanism of the dependence of rupture force on loading rate is also analyzed. We identify three reaction regimes in terms of loading rate: the regimes of equilibrium breaking/rebinding reactions, near-equilibrium reaction, and far from equilibrium with only bond breaking. These findings can help improve the current understanding of the stochastic behaviors of the adhesion clusters of molecular bonds under dynamic loading conditions.

Earthquakes occur as dynamic shear cracks and convert part of the elastic strain energy into radiated and dissipated energy. Local evolution of shear strength that governs this process, which is variable in space and time, can be studied from laboratory experiments and rupture models. At the same time, increasingly accurate measurements of radiated energy and other quantities characterize earthquakes in a rupture-averaged way. Here, we present and study two approaches to averaging frictional dissipation during dynamic rupture. The first one is based on the actual progression of dissipation, but the associated averaged shear stress does not reflect the local friction behavior. The second one is constructed to preserve prevailing features of local stress-slip response and performs well in the examples studied. The developed approach should be useful for visualizing energy partitioning in dynamic models and linking them to observations using diagrams that reflect dominant features of local stress evolution.

We study volumetric deformation structures in stepover regions using numerical simulations and field observations, with a focus on small-scale features near the ends of rupture segments that have opposite-polarity from the larger-scale structures that characterize the overall stepover region. The reversed-polarity small-scale structures are interpreted to be generated by arrest phases that start at the barriers and propagate some distance back into the rupture segment. Dynamic rupture propagating as a symmetric bilateral crack produces similar (anti-symmetric) structures at both rupture ends. In contrast, rupture in the form of a predominantly unidirectional pulse produces pronounced reversed-polarity structures only at the fault end in the dominant propagation direction. Several observational examples at different scales from strike-slip faults of the San Andreas system in southern California illustrate the existence of reversed-polarity secondary deformation structures. In the examples shown, relatively-small pressure-ridges are seen only on one side of relatively-large extensional stepovers. This suggests frequent predominantly unidirectional ruptures in at least some of those cases, although multisignal observations are needed to distinguish between different possible mechanisms. The results contribute to the ability of inferring from field observations on persistent behavior of earthquake ruptures associated with individual fault sections.

Geophysical observations have shown that transient slow slip events, with average slip speeds v on the order of 10 −8 to 10 −7 m/s, occur in some subduction zones. These slip events occur on the same faults but at greater depth than large earthquakes (with slip speeds of order ∼ 1 m/s). We explore the hypothesis that whether slip is slow or fast depends on the competition between dilatancy, which decreases fault zone pore pressure p, and thermal pressurization, which increases p. Shear resistance to slip is assumed to follow an effective stress law τ = f ( σ - p ) ≡ f σ ¯ . We present two-dimensional quasi-dynamic simulations that include rate-state friction, dilatancy, and heat and pore fluid flow normal to the fault. We find that at lower background effective normal stress ( σ ¯ ), slow slip events occur spontaneously, whereas at higher σ ¯ , slip is inertially limited. At intermediate σ ¯ , dynamic events are followed by quiescent periods, and then long durations of repeating slow slip events. In these cases, accelerating slow events ultimately nucleate dynamic rupture. Zero-width shear zone approximations are adequate for slow slip events but substantially overestimate the pore pressure and temperature changes during fast slip when dilatancy is included.

The boundary integral equation method (BIEM) has been applied to the analysis of rupture propagation of nonplanar faults in an unbounded homogeneous elastic medium. Here, we propose an extended BIEM (XBIEM) that is applicable in an inhomogeneous bounded medium consisting of homogeneous sub-regions. In the formulation of the XBIEM, the interfaces of the sub-regions are regarded as extended boundaries upon which boundary integral equations are additionally derived. This has been originally known as a multiregion approach in the analysis of seismic wave propagation in the frequency domain and it is employed here for rupture dynamics interacting with medium interfaces in time domain. All of the boundary integral equations are fully coupled by imposing boundary conditions on the extended boundaries and then numerically solved after spatiotemporal discretization. This paper gives the explicit expressions of discretized stress kernels for anti-plane nonplanar problems and the numerical method for the implementation of the XBIEM, which are validated in two representative planar fault problems.

This brief note reports the results of a set of biaxial experiments on Al-6061-T6 tubes tested to rupture under radial stress paths of combined internal pressure and axial load. The experiments are then simulated with shell-type finite element models, in which several yield functions are calibrated and implemented and their performance evaluated against the experimental results.

This paper gives a short review of two different methods for life prediction at high temperature; namely continuum damage mechanics (CDM) and the linear life-fraction rule (LFR). It is well known that the class of CDM theories with a separable evolution law gives a life prediction in accordance with the LFR. However, it appears to be an open question if this is a necessary condition. It is here shown that in order for a CDM theory to comply with the LFR it must have a separable evolution law. That is, if we can assume that a material follows the LFR, it is necessary to chose a separable evolution law for this material. The reverse is also true, to get a life-fraction different from unity, we must chose a nonseparable evolution law.

The dynamic rupture process of a thin power-law type non-Newtonian liquid film on a cylinder has been analyzed by investigating the stability to finite amplitude disturbances. The dynamics of the liquid film is formulated using the balance equations including a body force term due to van der Waals attractions. The governing equation for the film thickness was solved by finite difference method as part of an initial value problem for spatial periodic boundary conditions. A decrease in the cylinder radius will induce a stronger lateral capillary force and thus will accelerate the rupture process. The influence of the power-law exponent on rupture is discussed.

An approximate method is developed for comparing various fiber configurations in a composite structure with the objective of achieving optimal resistance to creep failure. The class of composite structures addressed has a single family of long or continuous strong fibers embedded in a creeping matrix material, e.g., a polymer, metal, etc. Thus, the structure is locally transversely isotropic with the fiber orientation generally varying throughout the structure. The proposed method, intended as an early design tool, is based on an upper bound on creep rupture time and an associated representative failure stress. The latter is evaluated and compared for different fiber configurations, thereby identifying that with optimal creep rupture resistance. This approach allows a substantial saving in computational time by avoiding a detailed analysis of the actual failure process. Application is made to a fiber-reinforced thick-walled cylindrical pressure vessel.

The constitutive response and failure behavior of a W-Ni-Fe alloy over the strain rate range of 10 -4 to 5 X 10 5 s -1 is experimentally investigated. Experiments conducted are pressure-shear plate impact, torsional Kolsky bar, and quasi-static torsion. The material has a microstructure of hard tungsten grains embedded in a soft alloy matrix. Nominal shear stress-strain relations are obtained for deformations throughout the experiments and until after the initiation of localization. Shear bands form when the plastic strain becomes sufficiently large, involving both the grains and the matrix. The critical shear strain for shear band development under the high rate, high pressure conditions of pressure-shear is approximately 1–1.5 or 6–8 times that obtained in torsional Kolsky bar experiments which involve lower strain rates and zero pressure. Shear bands observed in the impact experiments show significantly more intensely localized deformation. Eventual failure through the shear band is a combination of grain-matrix separation, ductile matrix rupture, and grain fracture. In order to understand the effect of the composite microstructure and material inhomogeneity on deformation, two other materials are also used in the study. One is a pure tungsten and the other is an alloy of W, Ni, and Fe with the same composition as that of the matrix phase in the overall composite. The results show that the overall two-phase composite is more susceptible to the formation of shear bands than either of its constituents.