Behaviour of materials under shock loading conditions

Shock wave research is a multidisciplinary field. In materials science, it is used to study equation-of-state, phase transitions and mechanical properties. In material processing, synthesis, powder compaction, shock sintering, shock welding etc. have been the prominent applications. We have been doing shock wave research at Trombay during the last two decades. Recently, we have built a single-stage gas gun to generate shock pressures in samples. In this paper, we describe this facility and some work done on the interpretation of shock-induced phase transitions.     

Study the dynamic crack path in brittle material under thermal shock loading by phase field modeling

For a wide variety of quasi-brittle materials, the constitutive microplane models of damage are capable of describing the anisotropic development and growth of microcracks when materials exhibit inelastic response. Damage development in solids leads to the degradation of the macroscopic material stiffness and results in different response in loading and unloading. On the other hand, the constitutive microplane models of plasticity describe the anisotropic plastic sliding that originates macroscopic permanent deformation and remains upon unloading. For realistic modeling of these materials, in which both damage and plasticity mechanisms can evolve simultaneously, the microplane damage and plasticity models can be coupled in a systematic and robust manner. This work presents a theoretical formulation of a consistent framework to couple both microplane damage and plasticity models for triggering inelastic behavior (damage and plastic effects) in engineering materials. Throughout the derivation, it is specifically shown that the proposed derivation complies with the thermodynamical restrictions with regard to the assessment of the local energy dissipation based on the Clausius–Duhem inequality. Finally, the algorithmic treatment of the developed constitutive framework is outlined for its incorporation into incremental-iterative solution procedures using Newton–Raphson schemes and examined by means of simple benchmark examples.     

Damage of structural materials under complex low-cycle loading

On the basis of the concepts of the continuum mechanics of damage, we propose an engineering method for the analysis of the kinetics of accumulation of scattered defects in metallic structural materials under conditions of elastoplastic deformation and low-cycle fatigue. It is shown that, in the general case of complex loading for the complex stress state, it is reasonable to use the specific energy of additional stresses (with regard for the arc of plastic strains in a loading cycle) as a parameter of damage for two types of fracture (rupture and shear). __________ Translated from Problemy Prochnosti, No. 6, pp. 25–34, November–December, 2007.     

An equation of state for porous materials under shock loading

Based on the physical interpretation of the linear equation of state (EOS) of dense solids under shock loading, which relates particle and shock speeds asU _s=C _b+gU _p, the EOS for porous solids has been developed and is expressed asU _s*=ΨC _b*+g*U _p whereC _b* andg* are effective bulk sound speed and effective inverse ultimate volume strain respectively. Ψ is a pore collapse function introduced specially to differentiate loading and unloading behaviour.C _b* andg* are derived theoretically whereas Ψ is established empirically as Ψ=f(U _p,C _b). This EOS does not call for any experimentally established material constant to describe the effect of porosity. Also its ability to describe the unloading behaviour distinguishes it from the presently available equations of state.     

More on the behavior of soda lime glass under shock loading

A series of plate impact experiments with soda-lime glass specimens was performed in order to further investigate the complex behavior of this material in the 0–8 GPa range of shock loading. Using commercial manganin gauges we followed the stress histories and their different shapes as the stresses increase from 3.5 to about 8.0 GPa. In particular, we find that there are meaningful differences between the shapes of these signals at pressures below about 4.0 GPa, in between 4.0 and 6.0 GPa and above 6.0 GPa. We also gather more data on the fractured glass behind the fracture wave front, from our measured stress histories, and offer a new way to determine the Hugoniot elastic limit of this material, as well as other brittle solids.     

Plastic deformation of titanium alloys under simple loading and its mathematical modeling

Results of an experimental investigation of the regularities of plastic deformation of titanium alloys in a plane stress state are analyzed. Tests were performed by loading thin-walled tubular specimens by an axial force and internal pressure under conditions of a proportional increase in the loads. The alloys are found to be transversely isotropic materials whose isotropic surface coincides with the cylindrical surface of the specimen. The process of plastic deformation of the alloys under simple loading is shown to be described well by equations of a previously proposed deformation theory of the plasticity of transversely isotropic media. Translated from Problemy Prochnosti, No. 5, pp. 27–35, September–October, 1999.     

Evaluation of the strength of structural materials with cracks under complex loading

We develop an experimental procedure and geometry of the specimens for the evaluation of the characteristics of crack growth resistance of structural materials for various macromechanisms of fracture (modes I, II, and III). We plotted diagrams of the limiting-equilibrium state of a body containing a crack (its strength) under complex proportionally increasing loading.     

Mechanical and structural behavior of a swelling elastomer under compressive loading

Swelling elastomers are a new breed of advanced polymers, and over the last two decades they have found increasing use in drilling of difficult oil and gas wells, remediation of damaged wells, and rejuvenation of abandoned wells. It is important to know whether an elastomer type or a certain seal design will function properly and reliably under a given set of oil or gas well conditions. This paper reports the results of an experimental and numerical study conducted to analyze how compressive and bulk behavior of an actual oilfield elastomer changes due to swelling. Tests were carried out on ASTM-standard compression and bulk samples (discs) before swelling and after different swelling periods. Elastic and bulk modulii were experimentally determined under different swelling conditions. Shear modulus and Poisson’s ratio were estimated using derived isotropic relations. Cross-link chain density and number average molecular weight were obtained using predictive equations of polymer physics. Mechanical testing was also modeled and simulated using the nonlinear finite element package ABAQUS, material model being Ogden hyperelastic model with second strain energy potential.Values of elastic and shear modulus dropped by more than 90% in the first few days, and then remained almost constant during the rest of the 1-month period. Poisson’s ratio, as expected, showed a mirror behavior of a sharp increase in the first few days. Bulk modulus exhibited a fluctuating pattern; rapid initial decrease, then a slightly slower increase, followed by a much slower decrease. Salinity shows some notable effect in the first 5 or 6 days, but has almost no influence in the later days. As swelling progresses, chain density decreases, much more sharply in the first week and then showing almost a steady-state behavior. In contrast, cross-link average molecular weight increases with swelling (as expected), but in a slightly fluctuating manner. Very interestingly, Poisson’s ratio approaches the limiting value of 0.5 within the first 10 days of swelling, justifying the assumption of incompressibility used in most analytical and numerical models. In general, simulations results are in good agreement with experimental ones. Results presented here can find utility in selection of swelling elastomers suitable for a given set of field conditions, in improvement of elastomer-seal and swell-packer design, and in modeling and simulation of seal performance.     

Standardized mathematical expression for stress-strain relations of structural steel under monotonic and uniaxial tension loading

Summary Tension tests on 36 specimens of steel plates produced in Japan are carried out according to the testing method proposed by RILEM TC 83. The stress-strain curves obtained from the tests are mathematically expressed by determining the material constants included in a modified Menegotto-Pinto model. These results give standardized stress-strain relations with respect to SS41 and SM50A steels generally used in Japan as structural steels for building structures. These kinds of data are expected to be accumulated by many countries and should be then compared internationally to establish a more reasonable stress-strain relationship usable for structural analyses.     

Determination of the parameters of limit state model for structural materials under asymmetric high-cycle loading

The paper considers a procedure for the determination of the parameters of a limit state model for structural materials using a transcendental power function. The model is used to construct limiting stress amplitude diagrams for asymmetric high-cycle loading. The procedure has been tested by comparing the values of limit state model parameters obtained as a result of the basic experiment in pulsating loading cycle with the values calculated by the method of minimization of the sum-ofsquares functional of deviations of experimental diagrams from calculated ones.     

Modeling shock loading of multicomponent materials including bismuth

The behavior of multicomponent mixtures and alloys, including bismuth, under high dynamic loads is described by the thermodynamically equilibrium (TEC) model. For condensed phases, the Mie–Grüneisen-type equation of state with regard to the Grüneisen coefficient depending on temperature is used, and gas in pores is among the main environmental components. The model used makes it possible to calculate the behavior of bismuth and materials based on this element (mixtures and alloys) for pressures higher than 6 GPa in one-velocity and one-temperature approximations on the assumption that the pressure is identical for all phases. The calculation results have been compared with the known experimental data and the model calculations performed by different researchers for porosity values varying from 1 to 3. It has been indicated that the model reliably describes shock loading of solid and porous bismuth as well as multicomponent alloys containing bismuth.     

Inelasticity monitoring of structural materials by the resonance method

We have developed a method which provides monitoring of the inelasticity kinetics of polycrystal materials by variation of the stress-strain phase-shift angle in the locally loaded surface zone of the material under study. The proposed method allows one to determine current value of damage of investigated aluminum alloy under laboratory conditions of cyclic deformation by variation of statistical characteristics of phase-shift angle distribution. AMg6N aluminum alloy, which is a cyclically hardening material, was used in this study. Translated from Problemy Prochnosti, No. 3, pp. 124–133, May–June, 2009.     

S-wave tracing technique to investigate the damage and failure behavior of brittle materials subjected to shock loading

To reveal the intrinsic rules of dynamic damage and failure behavior for brittle materials subjected to shock loading, a so-called transversal shear wave tracing technique (SWT) is proposed and discussed in detail in the present paper based on the wave propagation theory and the combined compression–shear impact technique. The idea of the SWT method is to diagnose the material state at real time by measuring the propagation features of loading and unloading shear waves. By using SWT technique, the preliminary experimental results of fiber-reinforced cement (FCEM) with electromagnetic particle velocity gauges embedded in the sample at different locations are reported and analyzed. By tracing the shear wave propagation, it is found that the amplitude and speed of unloading shear wave (S⁻) are related to the damage degree of the material. Particularly, S⁻ vanishes when impact velocities exceed 197 m/s, which discloses clearly a transition point from damage state to failure state of FCEM. It is significant for there is no obvious cusp to indicate such transition on the Hugoniot of FCEM. Some further studies are needed for understanding and developing of SWT method.     

A method for investigating the strength characteristics of sheet materials under impulse loading

We propose a method for the determination of the strength characteristics of metallic and nonmetallic materials under conditions of repeated impulse loading. By using this method, one can apply impulse loading to the tested objects both directly from an inductor and by hydroimpact, i.e., transferring impact pulses via a contact liquid. The method of electric pulses used as a basis of the suggested method of loading enables us to realize gradual control over the power of pulses and the frequency of their repetition. Translated from Problemy Prochnosti, No. 5, pp. 122–125, September–October, 1997.     

A method for investigating the strength characteristics of sheet materials under impulse loading

We propose a method for the determination of the strength characteristics of metallic and nonmetallic materials under conditions of repeated impulse loading. By using this method, one can apply impulse loading to the tested objects both directly from an inductor and by hydroimpact, i.e., transferring impact pulses via a contact liquid. The method of electric pulses used as a basis of the suggested method of loading enables us to realize gradual control over the power of pulses and the frequency of their repetition.