Elastic-plastic Impact Research Articles

Mechanics of hypervelocity simultaneously launched distributed particles

Understanding the complex physics of micrometeoroid/orbital debris (MMOD) cluster impacts to spacecraft structures and particulate impacts such as dust, ice, rain, etc. to hypersonic vehicles is essential to ensure safe space travel and hypersonic flight. Hypervelocity impacts resulting from simultaneously launched distributed particles (SLDPs) can be used to realistically replicate such environments. A method to controllably launch and perform in-situ characterization of SLDPs has been developed and implemented. A powder-driven, 12.7 mm smooth-bore two-stage light gas gun was used to launch collections of 0.79 mm and 1.98 mm diameter 2017-T4 aluminum particles to group velocities ranging from 2.4–5.4 km/s. Ultra-high-speed images recorded at 1 MHz were processed using custom-developed two-dimensional digital particle tracking algorithms to characterize the airborne SLDP clusters. In addition, the three-dimensional (3D) features of the SLDP clusters were quantified using impacts to 1.59 mm thick 6061-T6 aluminum plates. Target damage and interactions between adjacent particle impact sites were studied using a combination of numerical simulations and post-impact forensic analyses. Characteristic Elastic Plastic Impact Computation code simulations were used to estimate critical nearest neighbor distances between impact sites below which damage interactions occur and to subsequently probe plastic damage coalescence. For a given particle diameter, the critical nearest neighbor distance was roughly twice the in-plane radial distance from the impact axis to the location of 1% equivalent plastic strain. The plate-thickness-to-particle-diameter ratio was found to affect the plastic strain field more than the crater/perforation size. The predicted crater geometry agreed well with 3D optical profilometry measurements of target impact sites. The approach developed in this work can be readily applied to other particle/target geometries, materials, and impact scenarios, including MMOD cluster impacts and environmental effects on hypersonic vehicles.

A study on energy conversion behavior of single-shot elastic-plastic impact during shot peen forming

A study on energy conversion behavior of single-shot elastic-plastic impact during shot peen forming

Simulation of dynamic contact during shot blasting of parts

Shot blasting consists in hardening of the parts surface layer or workpieces with a stream of solid particles, mainly in the form of hardened steel balls. The purpose of the work is to develop and test a method for calculating the parameters of an elastic-plastic dynamic contact during shot blasting of parts based on mathematical modeling. The research technique is based on the consideration of a three-stage model of workpiece deformation under elastic-plastic impact by a steel spherical indenter. At the initial stage, the deformation is carried out elastically. Then, under some dynamic load, in the near-surface layer of the impacted body, a region of plastic state is generated, surrounded by an elastically deformable material. With a further increase in the dynamic load above a certain characteristic value, the region of the plastic state comes to the surface of the impacted part. Subsequently, the process is characterized by elastic-plastic indentation of the indenter (shot) into the impacted part. A method for upper calculating estimate the parameters of the dynamic contact of steel shot with parts based on the energy theory of elastic-plastic impact has been developed. To separate the elastic and plastic components of the deformation energy, the velocity recovery factor upon impact was used. The deformable material is accepted at the final stage of deformation as an ideal elastic – plastic material obeying the Prandtl’s scheme. Analytical dependencies convenient for practical use are obtained, which allow one to make calculating estimate of the depth and diameter of the imprint. Estimated calculations of the depth of the indentation depending on the speed of exposure to steel shot for shot blasting of a number of structural carbon steels have been performed. The results of the research can be used in the educational process in the preparation of engineering personnel of the machine-building profile, as well as in engineering practice.

Effect of initial impact energy on contact stiffness in linear contact law of low velocity elastic-plastic impact

In this paper, the loading force-indentation curve of low-velocity impact between an elastic-plastic plate and an elastic-plastic sphere by finite element (FE) analysis is investigated. The impactor mass and impact velocity are varied to cover a wide range of initial impact energies. The comparisons between the linear contact law using theoretical contact stiffness and the FE results show much difference. Based on the observation of FE data, the practical contact stiffness is strongly affected by the initial impact energy due to the nonlinearity of practical contact stiffness in the elastic-plastic impact. The definition of the equivalent contact stiffness is proposed to obtain the practical contact stiffness for the elastic-plastic impact accurately. The relations between theoretical and equivalent contact stiffness are massively calculated by FE covering a wide range of initial impact energies. Based on the FE results of the relations, a coefficient to revise the theoretical contact stiffness is suggested and a piecewise expression of the coefficient is presented by curve-fitting approach. It is demonstrated that the revised contact stiffness agrees well with the practical contact stiffness. This revised contact stiffness is of great value in predicting the maximum impact force in low velocity elastic-plastic impact between elastic-plastic bodies.

Study on Intrinsic Influence Law of Specimen Size and Loading Speed on Charpy Impact Test.

Charpy impact energy/impact toughness is closely related to external factors such as specimen size. However, when the sample size is small, the linear conversion relationship between the Charpy impact energy of the sub-size and full-size Charpy specimens does not hold; the Charpy impact toughness varies with the size of the specimen and other factors. This indicates that studying the internal influence of external factors on impact energy or impact toughness is the key to accurately understanding and evaluating the toughness and brittleness of materials. In this paper, the effects of strain rate on the flow behavior and the effects of stress triaxiality on the fracture behavior of 30CrMnSiNi2A high-strength steel were investigated using quasi-static smooth bar and notched bar uniaxial tensile tests and Split Hopkinson Tensile Bar (SHTP). Based on the flow behavior and strain rate dependences of the yield behavior, a modified JC model was established to describe the flow behavior and strain rate behavior. Charpy impact tests were simulated using the modified JC model and JC failure model with the determined parameters. Reasonable agreements between the simulation and experimental results have been achieved, and the validity of the model was proved. According to the simulation results, the impact energy was divided into crack initiation energy, crack stability propagation energy and crack instability propagation energy. On this basis, the effects of striker velocity and specimen width on the energy and characteristic load of each part were studied. The results show that each part of the impact energy has a negligible dependence on the hammer velocity, but there is a significantly different positive linear relationship with the width of the sample. The energy increment of each part also showed an inverse correlation with the increase in the sample width. The findings reveal that the internal mechanism of Charpy impact toughness decreases with the increase in sample width; to a certain extent, it also reveals the internal reason why the linear transformation relationship of Charpy impact energy between sub-size specimens and standard specimens is not established when the specimens are small. The analytical method and results presented in this paper can provide a reference for the study of the dynamic behavior of high-strength steel, the relationship between material properties and sample size, and the elastic–plastic impact dynamic design.

Research on a multi-point impact test of single-layer spherical reticulated shell

In order to study the impact resistance performance of reticulated shell under multi-point impact load, the multi-point elastic-plastic impact and destructive impact test of Kiewitt 6 (K6) single-layer spherical reticulated shell are carried out. The dynamic strain of key members, the dynamic displacement and the dynamic acceleration of key nodes are recorded during the multi-point impact process. The equivalent size numerical model of the test model is established by using the ANSYS/LS-DYNA simulation program, and the test conditions are simulated and analyzed. The peak strain and strain time history curves of the key members, the peak displacement and displacement time history curves of the key nodes, and the peak acceleration and acceleration time history curves of the key nodes in the test and simulation conditions are compared and analyzed. The energy transformation and energy transmission in the entire process of impact are studied at the same time. Results indicated a good agreement between the simulation results and the experimental results, and the dynamic response of the structure has the same trend. The number and position of impact points have a greater influence on the dynamic response of the impact area, while the influence on the non-impact area is smaller. With the increase of the number of impact points, the strain and displacement of the impact area of the reticulated shell gradually increase, but the acceleration change has no clear trend. At the same time, the experiment verified three deformation modes of the reticulated shell structure under the multi-point impact load.

Numerical Simulation of the Effects of Strain Hardening Exponent with and without Strain Rate Sensitivity of Material on Normal Elastic Plastic Impact

The material behavior selection is an important factor governing the structural response analysis of transverse impact problems, such as impact force, indentation and local elastic plastic deformation. In the present paper, the effects of strain hardening exponent (n) and strain rate sensitivity (m) on the transient response were investigated for low impact velocity by the aid of finite element simulation using the Abaqus Software. Investigated parameters are impact force histories, indentation and plastic strain (PEEQ). Results showed that the effect of n values on required parameters is more pronounced, unlike strain rate sensitivity which has not a significant influence. As well, material behavior selection is essential for an accurate local plastic strain analysis.

Transient Impact Analysis of Elastic-plastic Beam with Strain-Rate Sensitivity

The impact response of an elastic-plastic beam is highly complicated in nonlinear transient dynamics especially when the material's plasticity is strain rate dependent. To reduce the efforts required for the computational analysis, an analytical-numerical model (hybrid model) is proposed for the analysis of the transient response of the beam to sphere impact. The model couples two sub-models, a combined discretization model and a refined contact model. Both the sub-models incorporate the material strain rate dependence. The combined discretization model discretizes the beam in length direction by a dynamic substructure technique and in thickness direction by a finite difference technique to capture the beam wave propagations along the length and the stress variations along the thickness. The refined contact model extends the BD model [1] to sphere-beam impacts by introducing a new representative contact strain rate and a new unloading law to avoided the force discontinuity at the inception of unloading. The hybrid model is validated by the laboratory test performed for low-velocity impacts and by the three-dimensional finite element (FE) analysis implemented for moderate-velocity and moderate high-velocity impacts. The validations show that the hybrid model is accurate, highly efficient and suitable for the parametric study, especially for the study of impact-induced wave effects. By using the hybrid model, tests and FE analyses, the influences of the material strain rate sensitivity are investigated by comparing to the results of elastic plastic impact simulations ignoring the effect of strain rate. It is found that the influence of the strain rate dependence on the contact force-indentation relation is significant even in the low-velocity impacts. The influences of the strain rate dependence on the contact duration and maximum contact force are small, even for the impact velocity up to 30 m/s. The influences of the strain rate dependence on other impact responses are small in the low-velocity impacts, and increase with increasing of the impact velocity. A parametric analysis is conducted to investigate the effects of the impact conditions on the contact duration and coefficient restitution. Their map structures are complicated, depending upon the mass ratio and the impact position. A jumping/falling phenomenon for the variations of the contact duration and coefficient of restitution is found, which are caused by the multiple impacts.

A strain rate-dependent enhanced continuum model for elastic-plastic impact response of metal-ceramic functionally graded composites

An enhanced continuum model considering the strengthening of strain rate is developed to explore the particle size-dependent responses of the metal-ceramic functionally graded composite plates subjected to a drop-weight impact. The continuum model explicitly accounts for the effects of geometrically necessary dislocations and strain rate by combining Taylor dislocation model and Johnson–Cook model. The plastic constitutive relation of metal-ceramic FGM is derived from the Tamura–Tomota–Ozowa model subjected to different strain rates. The elastic-plastic impact responses of SiC/Al functionally graded plates with the micron-scale particle sizes and compositional gradient exponents are studied under varied impact velocities. The comparison at the numerical results for the particle size effects in the SiC/Al functionally graded plates and the experimental data reported in references demonstrates validity of the proposed continuum model.

Elastic-plastic Shock Processes Similarity

In the process of working out the design of the object, preliminary studies are carried out, including modeling (mathematical, physical or a combination of them) and comprehensive tests. In physical modeling, based on the methods of the theory of similarity and dimensions, the preparatory stages are implemented on the basis of an adequate mathematical model of the object or an in-depth description of its physical features. During stand testing the most complex problem is the problem of simulating an excitation in the form of intense single shock pulse. In stand shock testing in the contact is usually set an elastic-plastic, impact deformed element (crusher). The semi-empirical theory of impact is based on the assumption that only local elastic-plastic deformations could be taken into account. The study of the impact process is first illustrated using the method of physical modeling. In this two independent criteria of similarity of the shock processes are substantiated. Then, based on the analysis and numerical solution of the differential equation of impact, it is shown that the dimensionless complex arising from the theory of similarity and dimensions can be used to separately determine the main parameters of the shock process for given shock conditions – the duration of the load front and the maximum values of the contact force (overload) and local deformation. The experimental data obtained by means of a vertical pneumatic shock stand, having a small spread relative to the calculated results, are presented. The features of the process in the case of elastic-plastic impact of an elongated, rod type body are briefly considered. The criterion allowing to estimate quantitatively the relative role of wave processes in this variant of impact is offered which enables to validate conditions of considering the impacting body as a solid one.

Measurement of contact force-deformation relation between two identical spheres during elastic-plastic impact

Measurement of contact force-deformation relation between two identical spheres during elastic-plastic impact

The non-stationary dynamic of a beam under the elastic-plastic impact of a conical indenter

The problem of impact interaction of a conical indenter with the surface of a steel beam under elastic-plastic deformation is considered. The analysis of the dynamic reaction of the beam to the impact is considered analytically and numerically. The analytical solution is based on the phenomenological model of conical indentation and the solution of wave equations of beam dynamics at impact. The numerical study of the indentation process was carried out using the ANSYS software. The dynamic response of the beam is analyzed for different geometric parameters and different values of strength characteristics. Such tasks are widely used in construction practice in the implementation of non-destructive methods of assessing the mechanical characteristics of structures.

Experimental and theoretical analyses of elastic-plastic repeated impacts by considering wave effects

Abstract Repeated impacts of a sphere against a slender beam have been analyzed theoretically and experimentally. The analyses were performed with regard to a repeated impact process of a sphere striking repeatedly at the midpoint of the beam. The impact results in a local plastically deformed region with depth that is an insignificantly small part of the elastic beam cross-section. The theoretical analysis has been done by combining ten different theoretical contact models with the theoretical method that considers approximately the wave effects induced by impacts. The issue under investigation is to compare the selected contact model and to study the wave effect on impact behavior. The numerical results of theoretical analysis have been compared with the experimental data, and show that there are large differences in the calculated results for impact behavior obtained from the various models. The theoretical and experimental results show that selecting the appropriate contact model is very important on predicting contact behavior. For the contact time, Hertz model and ML model match well with the experimental results. For the accumulated permanent indentation, MYC model matches well with the experimental results. For COR (coefficient of restitution), CYM, Stronge and KK models match the experimental data well as the initial impact velocity of the sphere v0 1.5 m/s. For the rebound velocity, KE and KK models match well with the experiments. For an overall consideration of elastic-plastic contact deformation behavior, MYC model is more adequate to deal with the repeated impact problem of elastic-plastic beam. Large differences have been found between the theoretical analysis with and without considering the wave effects. Without considering the wave effects, the theoretical predictions in COR and in the rebound velocity of the sphere are unreasonable. It is clear that the wave effect induced by impact is very important for elastic-plastic impact problems of flexible structures.

Non-destructive test of steel structures by conical indentation

The problem of mechanical properties measurement of steel structures by non-destructive method of impact cone indentation is considered. The method is based on analytical solution and experimental data of a problem of impact indentation by cone into elastic-plastic half-space. Non-destructive dynamic indentation method is one of more efficient for mechanical properties assessment because of compact instrument that makes it possible of measuring at any point of structure. The scheme of impact indentation was considered and the problem of elastic-plastic impact is solved. The device with a computer way of information processing was created and tested for determining the characteristics of the existing structures. The method was adopted and tested on bridge structures, butt welded joints, civil engineering structures and others.

Identification of contact parameters from elastic-plastic impact of hard sphere and elastic half space

The theoretical and experimental analysis described in this paper demonstrate a simple systematic procedure to determine the contact parameters between a spherical impactor and an elastic half space via impact tests. Two main contact parameters were measured at different velocities of impact, that is the time duration of contact and the maximum normal contact force. A general nonlinear contact model based on power law is used to extract the contact stiffness and frequency of contact resonance from these two main contact parameters. Experimental results were obtained and compared for three steel samples with different hardness numbers and impacted by different sphere diameters of 2.0, 2.5 and 3.5mm to investigate the limits of elastic deformation. Effect of the used sphere diameter on the contact parameters are shown. The test results show that the adopted model using independently measured material data can predict the contact parameters due to hard sphere impact with elastic half space. The general trend shows the increase of contact stiffness with the sphere diameter but the limits of elastic regime decrease.

A new subregion mesh method for the investigation of the elastic-plastic impact in flexible multibody systems

Impact processes between flexible bodies often lead to local stress concentration and wave propagation of high frequency. Therefore, the modeling of flexible multibody systems involving impact should consider the local plastic deformation and the strict requirements of the spatial discretization. Owing to the nonlinearity of the stiffness matrix, the reduction of the element number is extremely important. For the contact-impact problem, since different regions have different requirements regarding the element size, a new subregion mesh method is proposed to reduce the number of the unnecessary elements. A dynamic model for flexible multibody systems with elastic-plastic contact impact is established based on a floating frame of reference formulation and complete Lagrange incremental nonlinear finite-element method to investigate the effect of the elastic-plastic deformation as well as spatial discretization. Experiments on the impact between two bodies are carried out to validate the correctness of the elastic-plastic model. The proposed formulation is applied to a slider-crank system with elastic-plastic impact.

Dynamic impact model of plastic deformation between micro-particles and flat surfaces without adhesion

ABSTRACTThis article considers the normal elastic–plastic impact of micro-particles against a flat surface without adhesion, and a dynamic model of plastic deformation was developed to describe the rebound behavior of impacting particles. Analytical expression for restitution coefficient was obtained and it was validated by the experimental data in the literature. The effects of material properties and impact velocities on the rebound behavior were also discussed. The relationship of normal force, particle velocity, plastic deformation, and contact duration was derived. The results show that the evolution of the normal force for the elastic–plastic impact is asymmetric, and the contact time for the elastic–plastic impact is obviously longer than the equivalent perfectly elastic impact for a given impact velocity. It is also found that the evolutions of contact time and loading time varying with impact velocities are in good agreement with the experimental observations.Copyright © 2016 American Association...

Peculiarities of distribution of dynamic disturbances in composite rods

The paper deals with longitudinal elastic-plastic impact on a two-layer composite rod with a fixed opposite end. The composite rod consists of a soft layer (aluminum) and a hard layer (steel), with their position varying. The condition of the continuity of the particle velocity vector and the stress is met on the contact boundary of the rods. To describe the wave processes the grid-characteristic method is used which makes it possible to construct computational algorithms on the borders of the integration area and the interfaces correctly. The interaction of reflected and refracted stress waves at the interface of composite rods is analyzed.. The phenomena on the interface of composite rods are made more complicated by their interaction with the dynamics of changing both the applied external load and the stress waves reflected from the boundary surfaces. As a result of numerical studies we have shown the possibility of damages on the interface for an aluminum-steel composite rod and rapid decay of non-linear effects in the case of steel-aluminum. Positioning rods with specific mechanical characteristics in the order specified by the calculations, we found a possibility to control the level of dynamic loading of each individual element of the composite rod, and hence the operability of the whole composite rod.

An Eulerian multi-material scheme for elastic–plastic impact and penetration problems involving large material deformations

An Eulerian multi-material scheme is developed for studying elastic–plastic impact and penetration problems involving large material deformations and shock waves. It consists of a Lagrangian plus remap (onto the original mesh) strategy at each time-step. The stress components of each material in a mixed cell are computed independently by assuming a common strain-rate to all materials. Similarly, the energy of each material in a mixed cell is updated independently and the mean pressure is determined using volume weighted average. This simplified approach eliminates commonly used iteration based pressure relaxation procedures and equation of state (EOS) closure models to find an equilibrium pressure in a mixed cell. A similar procedure is used to find equivalent stress in a mixed cell. The volume fraction of each material in a mixed cell is updated using a volume-of-fluid (VOF) interface tracking scheme. A new predictor–corrector (PC) scheme is developed to integrate the governing equations of the proposed multi-material model. The remapping of the stress components of the individual materials is achieved by a combination of a second-order monotonic upwind scheme and the VOF method. It is demonstrated that, despite using a ‘simple’ volume weighted scheme for calculating the total mean stress in mixed cells, the proposed scheme yields reasonable agreement with known analytical and experimental results of various impact and penetration problems.

A variational iteration solution for elastic–plastic impact of polymer/clay nanocomposite plates with or without global lateral deflection, employing an enhanced contact law

In the present paper, characteristics of low/medium velocity impact responses of thin nanocomposite plates impacted by rigid spherical indenters are investigated. The plates may either have lateral deflections or resting on rigid substrates. It is obvious that for thin plates with transverse mobility subjected to impact with rigid indenters, the actual indentation value is much less than that predicted by the traditional Hertz-type laws. A modified contact law that takes into account effects of the plate thickness and boundary conditions is employed in the present research. The variational iteration method is employed to develop a closed form semi-analytical solution. In comparison with the available numerical solution procedures, convergence of the present solution scheme is much higher and the solution algorithm converges unconditionally. Therefore, novelties may be found in the treated subject, modeling procedure, and solution algorithm. Comparisons made with results of the available numerical procedures, reveal the efficiency and accuracy of the presented solution algorithm.