Time evolution of damage due to environmentally assisted aging in a fiber bundle model.

Damage growth in composite materials is a complex process which is of interest in many fields of science and engineering. We consider this problem in a fiber bundle model where fibers undergo an aging process due to the accumulation of damage driven by the locally acting stress in a chemically active environment. By subjecting the bundle to a constant external load, fibers fail either when the load on them exceeds their individual intrinsic strength or when the accumulated internal damage exceeds a random threshold. We analyze the time evolution of the breaking process under low external loads where aging of fibers dominates. In the mean field limit, we show analytically that the aging system continuously accelerates in a way which can be characterized by an inverse power law of the event rate with a singularity that defines a failure time. The exponent is not universal; it depends on the details of the aging process. For localized load sharing, a more complex damage process emerges which is dominated by distinct spatial regions of the system with different degrees of stress concentration. Analytical calculations revealed that the final acceleration to global failure is preceded by a stationary accumulation of damage. When the disorder is strong, the accelerating phase has the same functional behavior as in the mean field limit. The analytical results are verified by computer simulations.

Scaling laws for impact fragmentation of spherical solids.

We investigate the impact fragmentation of spherical solid bodies made of heterogeneous brittle materials by means of a discrete element model. Computer simulations are carried out for four different system sizes varying the impact velocity in a broad range. We perform a finite size scaling analysis to determine the critical exponents of the damage-fragmentation phase transition and deduce scaling relations in terms of radius R and impact velocity v(0). The scaling analysis demonstrates that the exponent of the power law distributed fragment mass does not depend on the impact velocity; the apparent change of the exponent predicted by recent simulations can be attributed to the shifting cutoff and to the existence of unbreakable discrete units. Our calculations reveal that the characteristic time scale of the breakup process has a power law dependence on the impact speed and on the distance from the critical speed in the damaged and fragmented states, respectively. The total amount of damage is found to have a similar behavior, which is substantially different from the logarithmic dependence on the impact velocity observed in two dimensions.

Microstructure of damage in thermally activated fracture of Lennard-Jones systems.

We investigate the effect of thermal fluctuations on the critical stress and the microstructure of damage preceding macroscopic fracture of Lennard-Jones solids under a constant external load. Based on molecular dynamics simulations of notched specimens at finite temperatures, we show that the crystalline structure gets distorted ahead of the crack in the secondary creep regime. The damage profile characterizing the spatial distribution of lattice distortions is well described by an exponential form. The characteristic length of the exponential form provides the scale of damage, which is found to be an increasing function of the temperature: At low temperatures, damage is strongly localized to the crack tip, while at high temperatures, damage extends to a broader range, leading to more efficient relaxation of overloads. As a consequence, the stress intensity factor decreases with increasing temperature. The final macroscopic failure of the system occurs suddenly and is initiated by the creation of vacancies and voids. The creep strength exhibits inverse square root scaling with the notch size corrected by the extension of the process zone.

New universality class for the fragmentation of plastic materials.

We present an experimental and theoretical study of the fragmentation of polymeric materials by impacting polypropylene particles of spherical shape against a hard wall. Experiments reveal a power law mass distribution of fragments with an exponent close to 1.2, which is significantly different from the known exponents of three-dimensional bulk materials. A 3D discrete element model is introduced which reproduces both the large permanent deformation of the polymer during impact and the novel value of the mass distribution exponent. We demonstrate that the dominance of shear in the crack formation and the plastic response of the material are the key features which give rise to the emergence of the novel universality class of fragmentation phenomena.

Inhibition of mesothelin-CA-125 interaction in patients with mesothelioma by the anti-mesothelin monoclonal antibody MORAb-009: Implications for cancer therapy.

BACKGROUND: Mesothelin, a tumor differentiation antigen highly expressed in mesothelioma and ovarian cancer, is the receptor for CA-125 (MUC 16) and this interaction may play a role in tumor metastasis. MORAb-009 is a chimeric anti-mesothelin monoclonal antibody. METHODS: Twenty-four patients with mesothelin expressing cancers were treated on a phase I study of MORAb-009 administered as an intravenous infusion (12.5-400mg/m(2)) weeklyx4 doses with 2 weeks off before the next cycle. This report summarizes the effect of MORAb-009 on serum CA-125 kinetics in the eight patients with mesothelioma who had CA-125 levels measured before and at different time-points following therapy. RESULTS: MORAb-009 treatment led to a marked increase in serum CA-125 levels in all patients including those without elevated CA-125 levels before therapy. The increase in CA-125 levels was not due to disease progression since CA-125 levels decreased rapidly after stopping MORAb-009 therapy. No patients had signs of peritoneal or pleural inflammation as the possible cause of CA-125 rise. In addition, the elevated CA-125 levels were not due to MORAb-009 interfering with the laboratory assay used to measure CA-125. CONCLUSION: The increase in serum CA-125 produced by treatment with MORAb-009 is most likely due to MORAb-009 inhibiting the binding of tumor shed CA-125 to mesothelin present on mesothelial cells lining the pleural and peritoneal cavities. Inhibiting the mesothelin-CA-125 interaction could be a useful strategy to prevent tumor metastasis in mesotheliomas and ovarian cancer.

Avalanche dynamics of fiber bundle models.

We present a detailed analytical and numerical study of the avalanche distributions of the continuous damage fiber bundle model (CDFBM). Linearly elastic fibers undergo a series of partial failure events which give rise to a gradual degradation of their stiffness. We show that the model reproduces a wide range of mechanical behaviors. We find that macroscopic hardening and plastic responses are characterized by avalanche distributions, which exhibit an algebraic decay with exponents between 5/2 and 2 different from those observed in mean-field fiber bundle models. We also derive analytically the phase diagram of a family of CDFBM which covers a large variety of potential avalanche size distributions. Our results provide a unified view of the statistics of breaking avalanches in fiber bundle models.

Fragmentation processes in impact of spheres.

We study the brittle fragmentation of spheres by using a three-dimensional discrete element model. Large scale computer simulations are performed with a model that consists of agglomerates of many particles, interconnected by beam-truss elements. We focus on the detailed development of the fragmentation process and study several fragmentation mechanisms. The evolution of meridional cracks is studied in detail. These cracks are found to initiate in the inside of the specimen with quasiperiodic angular distribution. The fragments that are formed when these cracks penetrate the specimen surface give a broad peak in the fragment mass distribution for large fragments that can be fitted by a two-parameter Weibull distribution. This mechanism can only be observed in three-dimensional models or experiments. The results prove to be independent of the degree of disorder in the model. Our results significantly improve the understanding of the fragmentation process for impact fracture since besides reproducing the experimental observations of fragment shapes, impact energy dependence, and mass distribution, we also have full access to the failure conditions and evolution.

Critical ruptures in a bundle of slowly relaxing fibers.

We study the damage enhanced creep rupture of disordered materials by means of a fiber bundle model. Broken fibers undergo a slow stress relaxation modeled by a Maxwell element whose stress exponent m can vary in a broad range. Under global load sharing we show that due to the strength disorder of fibers, the lifetime t(f) of the bundle has sample-to-sample fluctuations characterized by a log-normal distribution independent of the type of disorder. We determine the Monkman-Grant relation of the model and establish a relation between the rupture life t(f) and the characteristic time t(m) of the intermediate creep regime of the bundle where the minimum strain rate is reached, making possible reliable estimates of t(f) from short term measurements. Approaching macroscopic failure, the deformation rate has a finite time power law singularity whose exponent is a decreasing function of m. On the microlevel the distribution of waiting times is found to have a power law behavior with m-dependent exponents different below and above the critical load of the bundle. Approaching the critical load from above, the cutoff value of the distributions has a power law divergence whose exponent coincides with the stress exponent of Maxwell elements.

Universality behind Basquin's Law of Fatigue.

Basquin's law of fatigue states that the lifetime of the system has a power-law dependence on the external load amplitude, tf approximately sigma 0- alpha, where the exponent alpha has a strong material dependence. We show that in spite of the broad scatter of the exponent alpha, the fatigue fracture of heterogeneous materials exhibits universal features. We propose a generic scaling form for the macroscopic deformation and show that at the fatigue limit the system undergoes a continuous phase transition. On the microlevel, the fatigue fracture proceeds in bursts characterized by universal power-law distributions. We demonstrate that the system dependent details are contained in Basquin's exponent for time to failure, and once this is taken into account, remaining features of failure are universal.

Computer simulation of fatigue under diametrical compression.

We study the fatigue fracture of disordered materials by means of computer simulations of a discrete element model. We extend a two-dimensional fracture model to capture the microscopic mechanisms relevant for fatigue and we simulate the diametric compression of a disc shape specimen under a constant external force. The model allows us to follow the development of the fracture process on the macrolevel and microlevel varying the relative influence of the mechanisms of damage accumulation over the load history and healing of microcracks. As a specific example we consider recent experimental results on the fatigue fracture of asphalt. Our numerical simulations show that for intermediate applied loads the lifetime of the specimen presents a power law behavior. Under the effect of healing, more prominent for small loads compared to the tensile strength of the material, the lifetime of the sample increases and a fatigue limit emerges below which no macroscopic failure occurs. The numerical results are in a good qualitative agreement with the experimental findings.

Scaling behavior of fragment shapes.

We present an experimental and theoretical study of the shape of fragments generated by explosive and impact loading of closed shells. Based on high speed imaging, we have determined the fragmentation mechanism of shells. Experiments have shown that the fragments vary from completely isotropic to highly anisotropic elongated shapes, depending on the microscopic cracking mechanism of the shell. Anisotropic fragments proved to have a self-affine character described by a scaling exponent. The distribution of fragment shapes exhibits a power-law decay. The robustness of the scaling laws is illustrated by a stochastic hierarchical model of fragmentation. Our results provide a possible improvement of the representation of fragment shapes in models of space debris.

Simple beam model for the shear failure of interfaces.

We propose a model for the shear failure of a glued interface between two solid blocks. We model the interface as an array of elastic beams which experience stretching and bending under shear load and break if the two deformation modes exceed randomly distributed breaking thresholds. The two breaking modes can be independent or combined in the form of a von Mises-type breaking criterion. Assuming global load sharing following the beam breaking, we obtain analytically the macroscopic constitutive behavior of the system and describe the microscopic process of the progressive failure of the interface. We work out an efficient simulation technique which allows for the study of large systems. The limiting case of very localized interaction of surface elements is explored by computer simulations.

Structure formation in a binary monolayer of dipolar particles.

We propose an experimental technique for an easy to control realization of a binary dipolar monolayer where the two components have oppositely oriented dipole moments constrained perpendicular to the plane of motion without the application of an external field. The experimental setup ensures that hydrodynamic effects do not play a crucial role in the structure formation, the particles move deterministically due to the dipole-dipole interaction. At low concentrations, cluster-cluster aggregation occurs with chainlike morphologies, while at high concentration the particles self-assemble into various types of binary crystal lattices, in good agreement with the theoretical predictions. The structures formed by the particles are found to be sensitive to external perturbations due to the central interparticle forces, however, static friction arising at the contact surface of particles can increase the stability compared to systems with only viscous friction.

Breakup of shells under explosion and impact.

A theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material is presented. Experiments were performed on eggshells under two different loading conditions: fragmentation due to an impact with a hard wall and explosion by a combustion mixture giving rise to power law fragment size distributions. For the theoretical investigations a three-dimensional discrete element model of shells is constructed. Molecular dynamics simulations of the two loading cases resulted in power law fragment mass distributions in satisfactory agreement with experiments. Based on large scale simulations we give evidence that power law distributions arise due to an underlying phase transition which proved to be abrupt and continuous for explosion and impact, respectively. Our results demonstrate that the fragmentation of closed shells defines a universality class, different from that of two- and three-dimensional bulk systems.

Structure of magnetic noise in dynamic fracture.

We present an experimental study of magnetic emission spectra recorded during impact fracture of steel. Novel features of dynamic fracture are revealed, i.e., the distribution of the voltage signals of the spectra; furthermore, the areas and energies of voltage peaks exhibit a power law behavior. The value of the exponents of the distributions proved to be characteristic for the failure mode: ductile failure gives rise to exponents significantly higher than brittle failure. The results imply that magnetic crackling noise accompanying impact fracture has a scale invariant structure which reveals new aspects of the dynamics of the fracture process.

Fragmentation of shells.

We present a theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material. Experiments were performed on brown and white hen egg shells under two different loading conditions: impact with a hard wall and explosion by a combustible mixture. Both give rise to power law fragment size distributions. A three-dimensional discrete element model of shells is worked out. Based on simulations of the model, we give evidence that power law fragment mass distributions arise due to an underlying phase transition which proved to be abrupt for explosion and continuous for impact. We demonstrate that the fragmentation of closed shells defines a new universality class of fragmentation phenomena.

Structure formation in binary colloids.

A theoretical study of the structure formation observed very recently [W. D. Ristenpart, I. A. Aksay, and D. A. Saville, Phys. Rev. Lett. 90, 128303 (2003)] in binary colloids is presented. In our model solely the dipole-dipole interaction of the particles is considered, electrohydrodynamic effects are excluded. Based on molecular dynamics simulations and analytic calculations we show that the total concentration of the particles, the relative concentration, and the relative dipole moment of the components determine the structure of the colloid. At low concentrations the kinetic aggregation of particles results in fractal structures which show a crossover behavior when increasing the concentration. At high concentration various lattice structures are obtained in a good agreement with experiments.

Restructuring of force networks.

The compaction of granular packings or soils is a collective process which for higher densities becomes increasingly slower reaching glassy behaviour. We present a study of this problem from various points of view, in particular we will represent the evolving force network that percolates through the system by an inverse fiber rupture model.

Breakup of dipolar rings under a perpendicular magnetic field.

An experimental and theoretical study of the breakup process of rings, formed by magnetic microspheres, under the application of an external magnetic field perpendicular to the plane of the ring is presented. We found experimentally that when the value of the external magnetic field falls below a lower critical field the dipoles rotate in the ring without any distortion of the ring structure. However, exceeding the upper critical field causes sudden breakup of the ring into short chains aligned with the field. Between the lower and upper critical fields the system is in a metastable state, and hence, it is very sensitive to external perturbations. The spiral opening was found experimentally to be the lowest energy transition from the ring to the chain conformation. We worked out an analytic approach and we performed computer simulations, the results of which are in good agreement with experiments.

Bursts in a fiber bundle model with continuous damage.

We study the constitutive behavior, the damage process, and the properties of bursts in the continuous damage fiber bundle model introduced recently. Depending on its two parameters, the model provides various types of constitutive behaviors including macroscopic plasticity. Analytical results are obtained to characterize the damage process along the plastic plateau under strain controlled loading; furthermore, for stress controlled experiments we develop a simulation technique, and numerically explore the distribution of bursts of fiber breaks assuming an infinite range of interaction. Simulations revealed that under certain conditions power law distribution of bursts arises with an exponent significantly different from the mean field exponent 5/2. A phase diagram of the model characterizing the possible burst distributions is constructed.