Plastic Work Research Articles

Nonlinear plastic buckling analysis of Micro–Scale thin plates established on higher order mechanism-based strain gradient plasticity framework

The present study investigates a nonlinear plastic buckling analysis of microplate by using the Mechanism-based Strain Gradient (MSG) plasticity. The MSG as a higher order theory is based on the Taylor model of dislocation interaction, consisting a multiple plastic work hardening. It extends a virtual work postulating the existence of higher-order stress work-conjugate at the in-plane traction of the microplate to the plastic strain gradient. The energy minimizing method is applied to obtain plastic buckling critical forces per each length scales and plastic hardening exponents. An iterative quadratic extrapolation (IQE) is implemented for linearization of nonlinear terms generated due to spatial variations of constitutive equations. The results indicate significant dependence of the critical force on the length scale as well as plastic work hardening exponent. Verifications are carefully done among two limit states of the elastic case and particular plastic analysis of a macro plate.

Static and Dynamic Loading Behavior of Ti6Al4V Honeycomb Structures Manufactured by Laser Engineered Net Shaping (LENSTM) Technology.

Laser Engineered Net Shaping (LENSTM) is currently a promising and developing technique. It allows for shortening the time between the design stage and the manufacturing process. LENS is an alternative to classic metal manufacturing methods, such as casting and plastic working. Moreover, it enables the production of finished spatial structures using different types of metallic powders as starting materials. Using this technology, thin-walled honeycomb structures with four different cell sizes were obtained. The technological parameters of the manufacturing process were selected experimentally, and the initial powder was a spherical Ti6Al4V powder with a particle size of 45–105 µm. The dimensions of the specimens were approximately 40 × 40 × 10 mm, and the wall thickness was approximately 0.7 mm. The geometrical quality and the surface roughness of the manufactured structures were investigated. Due to the high cooling rates occurring during the LENS process, the microstructure for this alloy consists only of the martensitic α’ phase. In order to increase the mechanical parameters, it was necessary to apply post processing heat treatment leading to the creation of a two-phase α + β structure. The main aim of this investigation was to study the energy absorption of additively manufactured regular cellular structures with a honeycomb topology under static and dynamic loading conditions.

On the conversion of plastic work to heat in Mg alloy AZ31B for dislocation slip and twinning deformation

In this study the conversion of plastic work to heat of a hot-rolled magnesium alloy AZ31B is investigated using a mechanism-based approach. Shear-compression specimen loading orientations are selected to promote plastic deformation principally through either basal slip, combined pyramidal and prismatic slip, or extension twinning. Loading orientations were selected based on predictions from a crystal plasticity model. High strain-rate adiabatic deformation was accomplished using a compression Kolsky bar. During each experiment the deforming gauge section temperature rise is recorded using a single-point infra-red detector. From the specimen deformation, thermal measurements, and crystal plasticity calculations of mechanism activity, the conversion of plastic work to heat was inferred. Specimens where basal, prismatic, and pyramidal slip accounted for the majority of plastic deformation exhibited similar percentage of plastic work converted to heat. Specimens where extension twinning was highly active exhibited a comparatively lower fraction of plastic work converted to heat.

Fracture behaviour of laser-welded 2219-T6 aluminium alloy under pulsed Lorentz force

Electromagnetic forming is a high-speed forming technology, using pulsed Lorentz force to make sheet metal deformed. The fracture behaviour of material during electromagnetic forming is a significant scientific issue in the development of this technology. In the current work, experimental methods are used to investigate the properties and microstructure of laser-welded 2219-T6 aluminium alloy and the fracture behaviour of the weld joint under pulsed Lorentz force. The results indicate that the hardness, strength, ductility, impact toughness of the laser-welded joint are all worse than that of the base metal because of the inhomogeneity of the microstructure and the existence of coarse brittle eutectic phases. This leads to the ductile fracture of laser-welded joint at the initial stage, followed by the sparking and partially melting breaking phenomena, under the pulsed Lorentz force. The molten structure is also observed on the fracture surface of the weld joint after electromagnetic tensile test rather than mechanical high-speed tensile test. During the fracture process under pulsed Lorentz force, local short circuits occur at the ductile crack tip of the weld joint due to the eddy current effect, resulting in the melting of the weld metal. The percentage reduction of area and the dimple sizes in the fracture morphology of the specimen under the conditions of high-speed deformation are larger than that under the condition of quasi-static tensile test, indicating the slight improvement in ductility of the laser-welded joint under high-speed deformation due to the inertial effect and the adiabatic temperature rise from the plastic work. Particularly, the above indicators are even larger under electromagnetic tensile test, revealing extra very slight increase in ductility compared with mechanical high-speed tensile test because of the body force and the additional temperature rise resulting from the Joule heat.

Finite element analysis of thermomechanical behavior and residual stresses in cold flowformed Ti6Al4V alloy

Ti6Al4V alloy is very hard to flowform at room temperature due to its limited ductility. However, it retains excellent adiabatic heat trapping and thermal softening abilities, which can play an important role in improving the formability. In this paper, a 3-D finite element model of backward flowforming with three staggered rollers has been developed in Abaqus/explicit to study the thermomechanical behavior and the residual stress evolution. The model has been validated via flowforming experiments. The role of the heat generation due to plastic deformation is highlighted by comparing a thermomechanical analysis to a purely mechanical analysis without incorporating the additional heat input due to the plastic work. The maximum predicted temperature rise during cold flowforming is 911 °C, which significantly reduces the flow stress in the deformation zone. The two most important factors, which affect the temperature rise in the deformation zone, are friction coefficient and coolant heat transfer coefficient. Hence, a study has been done to assess the sensitivity of the thermomechanical behavior and the residual stresses towards these factors. The friction between the mating surfaces is helpful, but a friction coefficient higher than 0.1 causes through-thickness strain heterogeneity. An increase in the friction coefficient reduces the residual stresses, while an increase in the convective heat transfer coefficient causes a transition from compressive to tensile residual stress along the thickness of the tube.

Non-parametric shape design optimization of elastic-plastic shear panel dampers under cyclic loading

In this work, we develop a non-parametric shape optimization method for designing low yield steel shear panel dampers (SPDs) under cyclic loading to enhance their energy dissipation capacity and verify it by experiments. Considering material nonlinearity (elastic-plastic) and geometric nonlinearity (large deformation), we formulate a shape optimization problem based on the variational method for 3D solid continua under cyclic loading, in which the plastic work in terms of von Mises equivalent stress is used as the objective function under a volume constraint. Considering the optimality conditions for the plastic work maximization problem, we theoretically derive the shape gradient function based on the Lagrange multiplier method, the material derivative formula, and the adjoint variable method. The derived shape gradient function is used to the H1 gradient method for designing the optimal shapes of 3D solid continua. We apply the developed shape optimization method to design SPDs made of low yield steel, which is an elastic-plastic material owning high-energy dissipation capacity. Cyclic enforced displacements acting on SPDs are used for simulating cyclic loading and evaluating the capacity of energy absorption of SPDs. To evaluate the nonlinear finite element analysis, we also perform cyclic loading test on SPDs. Two design examples of SPDs without and with holes are optimized to verify the validity of the developed shape optimization method. The results show that the developed optimization method works effectively to enhance the plastic work of SPDs. As a feature, this method can design SPDs more efficiently when considering the variation in the thickness direction.

Micromechanical modeling of the effects of adiabatic heating on the high strain rate deformation of polymer matrix composites

Fiber reinforced polymer matrix composites are increasingly being used to fabricate energy-absorbing aerospace structural components susceptible to impact loading, such as jet engine containment structures subjected to blade-out events. The development and certification of such structures necessitates a detailed understanding of the dynamic behavior of the constituent materials, particularly the strain rate, temperature, and pressure dependent polymer matrix, and their complex interaction. As the rate of deformation increases, the thermodynamic condition transitions from isothermal to adiabatic. The conversion of plastic work to heat causes local adiabatic heating in the polymer matrix, but the rapid nature of impact events does not allow sufficient time for heat to dissipate; ballistic impact events can therefore be regarded as fully adiabatic. Local adiabatic heating can significantly affect the high rate deformation response if thermal softening effects outweigh strain and strain rate hardening effects and therefore, must be explicitly modeled at the appropriate length scale. In this paper, an existing isothermal viscoplastic strain rate and pressure-dependent polymer constitutive formulation is extended to nonisothermal conditions by modifying the inelastic strain rate tensor components to explicitly depend on temperature based on the Arrhenius equation for nonisothermal processes. A methodology based on shifting neat resin dynamic mechanical analysis data is utilized to determine the polymer elastic properties over a range of strain rates and temperatures. Temperature rises due to the conversion of plastic work to heat are computed, assuming adiabatic conditions. It is demonstrated that the modified polymer constitutive model is capable of capturing strain rate and temperature dependent yield as well as thermal softening associated with the conversion of plastic work to heat at high rates of strain. The nonisothermal polymer constitutive model is then embedded within the Generalized Method of Cells micromechanics framework to investigate the manifestation of matrix thermal softening, due to the conversion of plastic work to heat, on the high strain rate response of a T700/Epon 862 unidirectional composite. Adiabatic model predictions for high strain rate composite longitudinal tensile, transverse tensile, and in-plane shear loading are presented. Results show a substantial deviation from isothermal conditions; significant thermal softening is observed for matrix dominated deformation modes (transverse tension and in-plane shear), highlighting the importance of accounting for local adiabatic heating in the polymer matrix in the high strain rate analysis of polymer matrix composite structures.

On the estimation of the elastoplastic work needed to initiate crack tearing

Plastic zones (pz) ahead of crack tips are obtained by incremental elastoplastic (EP) finite element (FE) 3D calculations for cracked components with relatively high and low transversal constraints, considering all effects associated with their geometry and loading conditions. Contrary to what is assumed in traditional Fracture Mechanics estimates, pz sizes and shapes do not depend only on the given crack driving force K or J. They depend as well on usually neglected geometric and load parameters such as the component width-to-thickness W/B, the crack size-to-component width a/W, and in particular the nominal stress-to-yield strength σn/SY ratios. Since damage ahead of the crack front depends on the plastic work spent inside the pz, this fact can have a major importance in practical applications, including in fatigue and in EP fracture estimates. This work proposes a methodology for evaluating pz volumes based on a sub-modeling FE analysis that uses the influence volume around a plastified Gauss integration point, instead of the entire plastified FE. This technique is then used to estimate the resistance to crack tearing initiation, assuming it can be obtained from the EP work spent inside the pz. Such estimates are validated using the ratio of experimental fracture toughness at the threshold of crack tearing for different W/B, a/W, and σn/SY combinations.

Microstructural evolution of a steam-turbine rotor subjected to a water-quenching process: numerical simulation and experimental verification

Cr-Ni-Mo-V steam-turbine rotors have been widely used as key components in power plants. In this study, a coupled thermomechano-metallurgical model was proposed to simulate the phase transformation and transformation-induced plasticity (TRIP) of a 30Cr2Ni4MoV steam-turbine rotor during a water-quenching process, which was solved using a user defined material mechanical behavior (UMAT) subroutine in ABAQUS. The thermal dilation, heat generation from plastic work, transformation latent heat, phase transformation kinetics, and TRIP were considered in the model. The thermomechanical portion of the model was used to predict the evolution of temperature, strain, and residual stress in the rotor. The phase transformation that occurred during the quenching process was considered. Constitutive models of phase transformations (austenite to pearlite, austenite to bainite, and austenite to martensite) and TRIP were developed. Experimental data were adopted and compared with the predicted results to verify the accuracy of the model. This demonstrates that the model is reliable and accurate. Then, the model was utilized to predict the temperature variation, dimensional change, minimum austenitization time, residual stress, TRIP, and volume fractions of each phase. It is concluded that this model can be a useful computational tool in the design of heat-treatment routines of steam-turbine rotors.

A new model for permanent flexural deflection of cantilever MEMS actuator by conventional mechanism-based strain gradient plasticity framework

In two past decades, there are so many works representing to elastic behaviors of cantilever MEMS actuators in the micro and nanoscales for various loading conditions and geometries. However, there are little efforts available for the permanent plastic behavior of the MEMS structures and actuators. In addition, the most size—dependent plasticity considerations based on gradient models have been limited to primary concepts on material modeling or microstructural evolution as compared with structural analyses. In this paper, a conventional mechanism-based strain gradient (CMSG) plasticity theory is applied to investigate permanent behavior of the cantilever micro-beam actuators, by determining the effect of length scale on flexural displacement. If the beam is scaled to micron size, mechanical behavior follows from material dimension or length scale. While the model consisted of a multiple plastic work hardening, its kinematics is established on the Euler–Bernoulli hypothesis. The deflection of cantilever MEMS actuator is determined for different cases of the loading and length scales, compared with other relevant theoretical and experimental observations. Also, the effect of the elastic medium of the environmental foundation is considered for the actuator, dedicatedly.

Time dependent nanomechanical properties of NiMnGa Heusler alloy

In this work nano-indentation has been adopted as a technique to measure the Time dependent deformation (TDD) and other related mechanical properties of NiMnGa Heusler alloys. The measurement of TDD utilizes two different techniques namely: CRL (Constant Rate of Loading) and CSR (Constant Strain Rate) modes. Tests to measure the behavioral dependence on the holding time were also done. The loading rates for CRL technique were varied from 0.1 mN/s to 1 mN/s. Strain rates for CSR mode were varied from 0.05 to 2. The tests were done at room temperature on Ni50Mn28Ga22 alloy which was prepared by TIG arc melting. Hardness and strain rate, both are inversely dependent on depth of indentation and time. The amount of plastic work was calculated and its dependence on loading rate, holding time and strain rate has been studied. The parabolic dependence of the fraction of plastic work to the time of holding was obtained by least squares method. The amount of recovery also declined as the loading rate and strain rates were increased. Microstructural studies were also performed to observe the changes that are inflicted underneath the surface during indentation. The microstructure was initially a twinned martensitic structure having two different variants which developed into a single martensitic variant under the influence of load. Nano twins were also observed in the microstructure.

Wetting improvement of plastic working plate for liquid desiccant dehumidification systems

Liquid desiccant dehumidification is promising because it removes extra excess effectively and environmentally. By affecting the contact area between desiccant and air, the mass transfer performance is significantly influenced by the wettability on inner working surfaces of the dehumidifier. Non-metallic surfaces such as plastics are considered as good alternatives due to their anticorrosion characteristics. However, poor wetting properties severely limited the application. In this study, a silica super-hydrophilic coating on pre-etched plastic surfaces was developed by the sol-gel method to enhance wetting performance. Coating properties were test on samples made of acrylic with a 40% LiBr solution and deionized water. Results showed that with the pre-etching and super-hydrophilic coating, water droplets could completely spread within 3 seconds, which means that the contact angle could be reduced to about 0 degrees. Furthermore, the durability test showed that after 48 hours of continuous scouring under 0.01 Mpa water pressure (approximately 1000 times that of that in common liquid desiccant systems), the droplet could fully spread within 22s and the contact angle remained was maintained at 0°. Therefore, the novel coating on pre-etched surfaces developed in this study could effectively increase the wetting performance on plastic surfaces, which is helpful to the mass transfer of liquid desiccant dehumidification systems.

A polycrystal plasticity based thermo-mechanical-dynamic recrystallization coupled modeling method and its application to light weight alloys

Hot forming often has to be resorted when processing metals with limited room-temperature formability, such as aluminum, magnesium, etc. The temperature rise induced by plastic work, especially under high strain rates, can exert significant effect on mechanical response as well as dynamic recrystallization of deformed metals. In the present work, a polycrystal plasticity based thermo-mechanical-dynamic recrystallization (DRX) coupled approach is established by implementing thermo-mechanical effect in a VPSC-DRX model where a grain nucleation and growth model is implemented into the VPSC framework. The modeling parameters associated with various slip modes, temperatures and strain rates are calibrated by isothermal compression experiments, and then evolution functions of hardening and DRX related parameters with respect to temperature and strain rate are established. The integrated computation of plastic deformation, texture, grain size and temperature update in hot deformation of metals can be achieved. The proposed method is verified and then applied to simulate hot extrusion processes of magnesium alloy bars at three different ram speeds. The influences of ram speed on development of deformation texture and grain size are analyzed. The temperature rise due to plastic work enhances stress softening and stimulates grain growth, makes the macro/micro responses of materials no longer monotonically varied with strain rate.

Numerical simulations of granular material behavior under rotation of principal stresses: micromechanical observation and energy consideration

A numerical investigation on the behavior of granular materials subjected to the rotation of principal stresses using the discrete element method is presented. A numerical procedure is developed to implement the two-dimensional arbitrary stress or strain paths imposed on polygonal specimens. Significant volumetric strain can be obtained and granular assembly appears to develop an anisotropic internal structure characterized by the contact-normal-based fabric tensor in due course, with its direction being rotated with the rotation of the principal stress. The observations indicate a significant degree of non-coaxiality between the principal-stress direction and the principal-strain increment direction. An ultimate state can be reached after sufficiently large numbers of cycling, resulting in a constant fabric norm and a circular strain trajectory in the deviatoric space. The boundary work, dissipation, and strain energy, are also registered during the entire loading process and its correlation between non-coaxial deformations is analyzed from micro-scale perspective. Before the ultimate state is reached, the applied work is partially dissipated by frictional sliding, and the remainder is stored as the strain energy within the specimen. When the ultimate state is reached, however, no change in the strain energy is obtained, and the plastic work is entirely dissipated, as the elastic portion of the free energy increment only depends on the elastic strain.

Великі пружно-пластичні деформації квадратних мембран під дією локалізованих імпульсних навантажень

Ductile isotropic materials are widely used in protective systems against transient pulse pressure loads, such as those of localised blasts. This is due to the combined elastic-plastic response which contributes to dissipation of total impulse from extensive loading as the energy stored elastically limits deformation while the energy expended plastically limits the level of transferred forces in the structure. In the case of thin, modern armour graded steel plates, the tailored metallurgy helps the structure store energy within the bounds of elastic region, which may be dissipated at a later stage as damping kills it off in subsequent cycles. On the other hand, the plastic work is almost entirely converted to heat and dissipates. The present work focuses on the elastic and plastic energies in the membrane and aims at deducing, from the minimization of Föppl-Von-Kármán (FVK) energy functional combined with enforcing the constitutive relations of limit analysis, the dynamic elastic-plastic response of localised blast loaded square membranes undergoing large deformations. The presumed blast load function is a multiplicative decomposition of a prescribed continuous piecewise smooth spatial function and an arbitrary temporal function which may assume various temporal shapes (e.g. rectangular, linear, exponential). Considering the elastic response, a single-degree-of-freedom model was developed from the prescribed displacement field and associated stress tensor having clamped and simply supported boundary conditions. The explicit closed form solutions were sought by using the Ritz-Galerkin’s variational method as well as the Poincaré-Lindstedt perturbation method. The theoretical solutions of rigid-perfectly plastic square membranes subjected to the same blast scenarios were then discussed. From the combined effects we deduce the load displacement curves representing the trajectory of the nonlinear elastic-perfectly plastic structure.

Influence of H2S Corrosion on Tensile Properties and Fracture Toughness of X80 Pipeline Steel

Tensile and fracture properties of X80 pipeline steel were studied in a mimic petrochemical environment. X80 pipeline steel specimens were firstly exposed to air or H2S corrosive medium. Then their tensile properties and δ-∆a resistance curves were obtained in experiments. The influence of H2S corrosion on the X80 pipeline steel’s crack growth resistance curve, fracture toughness, and plastic work loss was analyzed. The comparison between the test results after two pretreatments indicates that there was no significant difference in the X80 pipeline steel’s ultimate tensile strength before and after H2S corrosion. But fracture elongation, area reduction and fracture toughness varied greatly (a substantial decrease in elongation and reduction of area). The crack growth resistance curve of the specimen in air was obviously higher than the crack growth resistance curve of the corroded one. Under stable crack growth stage, the crack initiation toughness δ 0.2BL of the specimen in air was 0.732 mm, 2.02 times that of the corroded one (0.364 mm). In the case of similar crack growth ∆a, the plastic work required in the crack growing process (UP) of the specimen in air was 2.29 times that of the H2S-corroded specimen ( $$ {U}_P^{\hbox{'}} $$ ). H2S corrosion resulted in a significant reduction of the fracture toughness of X80 pipeline steel. Hence, H2S corrosion should be avoided in the process of natural gas transportation by pipelines, so as to protect the pipeline steel from toughness degradation.

Evaluation of the heat dissipated around the crack tip of AISI 422 and CF3M steels by means of thermography

The fatigue crack growth depends on the dissipated energy at the crack tip and in this regard, different analytical and numerical models were proposed by many researchers to describe as the plastic work affect the fatigue material behaviour. Experimental tests can be carried out for evaluating the energy dissipated during the crack growth principally based on the hysteresis loop measurement. However, these techniques need of suitable equipment and set-ups and then find some restrictions if applied in-situ and on real components.In this work, an experimental approach is used to obtain a thermographic parameter capable of describing the plastic work at the crack tip. The proposed approach is based on the phase shift of the thermal signal that occurs at the crack tip in the plastic area.Two specimens of two different steels, austenitic and martensitic, were tested and monitored with an infrared camera to collect thermoelastic phase data. A similar correlation to the dissipated energy was obtained with the fatigue crack growth behavior of materials.

Computational analysis of mesoscale thermomechanical ignition behavior of impacted LLM-105 based explosives.

LLM-105 (2,6-diamino-3,5-dinitropyrazine-1-oxide) is an insensitive high explosive crystal which has performance between that of HMX and TATB. An elastoviscoplastic dislocation model is developed for LLM-105 crystal, which accounts for the dislocation evolutions at the crystal interior and crystal wall and strain-rate dependent work hardening. Three different crystal morphology (cubic, icosahedral, rodlike) of LLM-105 based explosive computational models were constructed and subjected to an impact velocity of 200 m s−1 and 500 m s−1. Effects of crystal morphology and initial dislocation density on thermomechanical ignition behavior of LLM-105 based explosives were analyzed. Dislocation density of both crystal interiors and crystal walls in the rodlike LLM-105 based explosive increases slower than that in the cubic and icosahedral explosives. Both the volume averaged and localized stress and dislocation density are the lowest for the rodlike explosive. At the impact velocity of 500 m s−1, a temperature rise due to volumetric work, plasticity work and chemical reaction is sufficiently high to lead to the ignition of the cubic explosive, which shows that the rodlike explosive is the least sensitive among the three explosives. Moreover, with the increase of initial dislocation density, the corresponding volume averaged and localized stress and temperature increase as well. Results presented bridge the macroscale thermomechanical ignition response with the mesoscale deformation mechanisms, which is essential for better understanding the ignition mechanisms and guiding the design of LLM-105 based formulations.

Numerical investigation of the evolution of microstructure of nickel-based alloys during plastic working

The paper considers the process of hot plastic working of a large metal billet, which causes its upsetting to a dimension specified by the manufacturing technique and the average axial deformation of 32.5%. The billet was made of heat-resistant nickel alloy Waspalloy widely used in the aircraft industry. The structural condition of the deformed alloy and, consequently, its mechanical properties depend on many factors: the degree of deformation, the rate of deformation, recrystallization in the process of deformation. This generates a need for a comprehensive study of the plastic flow in the examined material and the influence of the deformation parameters on its characteristics. The paper presents the results of a numerical investigation of the deformation and temperature states of the billet that allowed us to analyze changes occurring in the structure of nickel alloy during plastic deformation at different upsetting rates (50 and 100 mm/s). The shape of billet lateral surface and the forces required to complete the process of free upsetting are calculated as well. The numerical simulation was performed by the finite element method using the DEFORM-2D/3D software package. The average grain size and the fraction of recrystallized grains in the body of the billet were determined based on the Johnson-Mehl-Avrami-Kolmogorov model (JMAK). The results of numerical modeling showed that the greatest change in the microstructure of the alloy occurs in the region of intense plastic strains. The upsetting rate of 100 mm/s leads to the formation of structure with finer grains compared to the structure formed at the upsetting rate of 50 mm/s.

Energy absorption of aluminum panels subjected to gelatin projectile impact

Abstract Digital image correlation (DIC) method has been widely used on dynamical experiments. This full-field and real-time method can fill in the gap of traditional point-based measurements of typical structures subjected to soft body impact such as bird strike. In order to get further understandings of soft body impact process, the present study analyzed the time-dependent energy exchange during impact experiments. The dynamic responses of the aluminum target panels were obtained using 3D digital image correlation method so that their displacement and strain field histories can be tracked. By introducing the material properties of the targets, their time-dependent stress state and consequently the strain energy can be calculated. With the help of time-dependent profiles of target panels, their energy absorption properties were theoretically analyzed, including the exchange of kinetic energy and plastic work. The results showed that when the impact loadings were increased, the plastic work generated by radial membrane force became the major source of energy dissipation. The transverse movements consumed more kinetic energies than rotatory moments. This research may provide a further application of DIC results and help to better understand the soft body impact process on targets with large deformations.