Effective Plastic Strain Rate Research Articles

Comprehensive investigation of microstructural inhomogeneity in the bonding zone of explosive-welded AISI 410S/A283GrD composite

ABSTRACT This study investigates the microstructural inhomogeneity in the bonding zone of AISI 410S/A283GrD explosive-welded plate by experiment and simulation. The interfacial microstructure and chemical components are investigated, and the difference of grain size across the peak and valley is studied separately. Due to severe plastic deformation and work hardening during the explosive welding process, the microhardness of the combination area adjacent to the interface is higher than that of parent plates. The wavy interface of the numerical simulation is in good agreement with the experimental observation. The numerical simulation results, such as distribution of shear stress, pressure, and effective plastic strain rate of the model are investigated, and the forming reason of interfacial microstructures, are explained by these results.

Effect of Curvature on Penetration Resistance of Polycarbonate Panels

Three-dimensional transient deformations of clamped flat and doubly curved polycarbonate (PC) panels impacted by a rigid smooth hemispherical-nosed circular cylinder have been numerically studied by the finite-element (FE) method to delineate effects of the panel radius of curvature to its thickness ratio on their penetration resistance. The PC is modeled as thermoelastoviscoplastic with the effective plastic strain rate depending upon the hydrostatic pressure. The effective plastic strain of 3.0 at failure is ascertained by matching for one set of flat panels the computed and the experimental minimum perforation speeds. It is found that a negative curvature (i.e., the center of curvature toward the impactor) of a panel degrades its penetration performance, and the positive curvature enhances it especially for thin panels with thickness/radius of curvature of 0.01. However, the benefit is less evident for panels with the panel thickness/radius of curvature of 0.04 or more. For positively curved thin panels, an elastic hinge forms around the central impacted area during an early stage of deformations, and subsequent deformations occur within this region. No such hinge is observed for flat plates, negatively curved panels of all the thicknesses, and positively curved thick panels. Furthermore, the maximum effective stress induced in regions surrounding the impacted area is less for positively curved panels than that for flat panels. The dominant failure mechanism is found to be the deletion of failed elements due to the effective plastic strain in them exceeding 3.0 rather than due to plug formation. For an example problem, the dependence of the effective plastic strain rate upon the hydrostatic pressure and the consideration of the Coulomb friction at the contact surfaces exhibited minimal effects on the penetration characteristics. This information should be useful for designers of impact-resistant transparent armor, such as an airplane canopy, automobile windshield, and goggles.

A thermodynamic modeling approach for dynamic softening in glassy amorphous polymers

Strain softening is highly dependent on the thermo-mechanical history. The degree of post-yield strain softening increases with the aging time, which is dependent on the aging temperature, and decreases with plastic strain. In this paper, we present two approaches to describe the strain softening. The first approach is an extension of the widely applied dynamic softening method that evolves the yield strength with the effective plastic strain rate. Though this approach can quantitatively capture the main experimental observations, it is empirical and does not capture the physical mechanism behind aging and strain softening. The second approach couples inelastic deformation with an evolution of the nonequilibrium state. The approach is based on the effective temperature nonequilibrium thermodynamic framework that introduces a thermodynamic state variable, the effective temperature to characterize the nonequilibrium state. The temperature-dependent evolution of the effective temperature describes the glass transition of amorphous polymers. We show that the physical aging and dynamic softening arise from the evolution of the effective temperature towards equilibrium and with plastic deformation towards a steady-state value away from equilibrium.

Numerical simulation of systems of shear bands in ductile metal with inclusions

We develop a method for numerical simulations of high strain-rate loading of mesoscale samples of ductile metal with inclusions. Because of its small-scale inhomogeneity, the composite material is prone to localized shear deformation (adiabatic shear bands). This method employs the Generalized Method of Cells of Paley and Aboudi [Mech. Materials, vol. 14, pp. 127–139, 1992] to ensure that the micro mechanical behavior of the metal and inclusions is reflected properly in the behavior of the composite at the mesoscale. To find the effective plastic strain rate when shear bands are present, we extend and apply the analytic and numerical analysis of shear bands of Glimm, Plohr, and Sharp [Mech. Materials, vol. 24, pp. 31–41, 1996]. Our tests of the method focus on the stress/strain response in uniaxial-strain flow, both compressive and tensile, of depleted uranium metal containing silicon carbide inclusions. We use the Preston-Tonks-Wallace viscoplasticity model [J. Appl. Phys., vol. 93, pp. 211–220, 2003], which applies to the high strain-rate regime of an isotropic viscoplastic solid. In results, we verify the elevated temperature and thermal softening at shear bands in our simulations of pure DU and DU/SiC composites. We also note that in composites, due the asymmetry caused by the inclusions, shear band form at different times in different subcells. In particular, in the subcells near inclusions, shear band form much earlier than they do in pure DU.

FEA of electromagnetic forming using a new coupling algorithm

Finite element modeling of electromagnetic forming includes modeling of mechanical aspects, modeling of electro- magnetic aspects, and a coupling method between the two models. The electromagnetic problem is to determine the magnetic pressure and its temporal and spatial distribution. Whereas the mechanical problem is to find out workpiece deformation result- ing from the magnetic pressure applied on this workpiece. Nonetheless complications in the simulation exist due to pressure variation with workpiece deformation. These difficulties can be resolved by using one of the known coupling algorithms; loose coupling, or strong coupling. But these coupling strategies either have low accuracy of results or take long simulation time. The current research introduces an enhanced loose coupling algorithm for simulation of electromagnetic sheet metals bulging. The proposed coupling strategy takes into account deformation effects on pressure without the need for solving the updated electromagnetic model every new time step. Comparison between present simulation results and experimental results of other researchers showed good agreement. Effective plastic strain, and effective plastic strain rate distribution and evolution were presented in addition to thickness and deflection evolution of the workpiece.

Evaluation of Associated and Non-Associated Flow Metal Plasticity; Application for DC06 Deep Drawing Steel

In this paper the capabilities of Associated Flow Rule (AFR) and non-AFR based finite element models for sheet metal forming simulations is investigated. In case of non-AFR, Hill’s quadratic function used as plastic potential function, makes use of plastic strain ratios to determine the direction of effective plastic strain rate. In addition, the yield function uses direction dependent yield stress data. Therefore more accurate predictions are expected in terms of both yield stress and strain ratios at different orientations. We implemented a modified version of the non-associative flow rule originally developed by Stoughton [1] into the commercial finite element code ABAQUS by means of a user material subroutine UMAT. The main algorithm developed includes combined effects of isotropic and kinematic hardening [2]. This paper assumes proportional loading cases and therefore only isotropic hardening effect is considered. In our model the incremental change of plastic strain rate tensor is not equal to the incremental change of the compliance factor. The validity of the model is demonstrated by comparing stresses and strain ratios obtained from finite element simulations with experimentally determined values for deep drawing steel DC06. A critical comparison is made between numerical results obtained from AFR and non-AFR based models

Fatigue Analysis of Forged Aerospace Components Based on Micro Structural Parameters

With the objective of creating a simulation model for the lifetime calculation of forged aerospace components it is necessary to clarify the damage mechanisms in the materials used. This has been researched for the Ni-base alloy Inconel 718 by varying the forging parameter effective plastic strain rate, which is realised by using three types of equipment: hydraulic press, screw press and hammer. Specimens processed at the screw press show the highest lifetime by keeping all other forging parameters unvaried. Micro structural investigations show that the amount and morphology of dominant as-large-as grains play a important role. This methodology is currently investigated for Ti-6Al-4V. Lifetime tests show that besides effective strain and anisotropy the influence of morphology is important. As soon as the model status allows lifetime analyses the thermo-mechanical process (forging and heat treatment) can be developed depending on the desired lifetime specifications in order to realise an interdisciplinary lifetime optimisation of forgings. A further aim is the use of basic coherences of safe-life and fail-safe approaches in the low and high cycle fatigue region in order to reasonable handle with flaws and defects at the edge layer.

Failure of Dynamically Loaded Thermoelastoviscoplastic Rectangular Plate

The initiation and propagation of a crack and an adiabatic shear band in three-dimensional finite coupled thermomechanical deformations of a homogeneous and isotropic thermoelastoviscoplastic rectangular 4340 steel plate containing a centrally located through-the-thickness elliptic void and deformed in simple tension are analyzed numerically by using the finite element computer code DYNA3D. Initially, the major and the minor axes of the elliptic void coincide with the centroidal axes of the plate. An element is assumed to have failed when the damage parameter defined in terms of histories of the effective plastic strain, the effective plastic strain rate, the triaxiality factor, and the temperature at its centroid equals one; an adiabatic shear band initiates at a point when the effective plastic strain there equals one, while the material point is deforming plastically and deformations of the surrounding material are inhomogeneous. It is found that the ratio R of lengths of the two principal axes of the void significantly influences when and where a crack and an adiabatic shear band initiate and which one initiates first They usually originate from a point on the surface of the elliptic void which is also on the midsurface of the plate, and they propagate faster in the thickness direction. An adiabatic shear band initiates sooner in the three-dimensional simulations than when displacements in the thickness direction are constrained to vanish. The crack tip follows a zigzag path that does not lie in one plane.

A viscoplastic strain gradient analysis of materials with voids or inclusions

A finite strain viscoplastic nonlocal plasticity model is formulated and implemented numerically within a finite element framework. The model is a viscoplastic generalisation of the finite strain generalisation by Niordson and Redanz (2004) [Journal of the Mechanics and Physics of Solids 52, 2431–2454] of the strain gradient plasticity theory proposed by Fleck and Hutchinson (2001) [Journal of the Mechanics and Physics of Solids 49, 2245–2271]. The formulation is based on a viscoplastic potential that enables the formulation of the model so that it reduces to the strain gradient plasticity theory in the absence of viscous effects. The numerical implementation uses increments of the effective plastic strain rate as degrees of freedom in addition to increments of displacement. To illustrate predictions of the model, results are presented for materials containing either voids or rigid inclusions. It is shown how the model predicts increased overall yield strength, as compared to conventional predictions, when voids or inclusions are in the micron range. Furthermore, it is illustrated how the higher order boundary conditions at the interface between inclusions and matrix material are important to the overall yield strength as well as the material hardening.

Strain rate effect on in-plane shear strength of unidirectional polymeric composites

The strain rate effect on the in-plane shear strength of unidirectional composites was investigated. Off-axis S2/8552 glass epoxy block specimens were employed to produce in-plane shear failure. In order to determine the strain rate effect, specimens were tested in compression at various strain rates. For strain rates less than 1/s, experiments were conducted on an MTS machine. For higher strain rates, they were performed using a Hopkinson pressure bar. Experimental observations indicated that, for composite specimens with off-axis angles less than 10°, fiber microbuckling is the dominant failure mechanism. However, for the specimens with off-axis angles between 15° and 45°, in-plane sharing is the major failure mode. If the off-axis angle is greater than 45°, out of plane shear failure would take place. Only the in-plane shear failure mechanism was concerned in this study. The shear strain rate was obtained from the uniaxial strain rate by relating the effective plastic strain rate to the plastic shear strain rate with the aid of a viscoplasticity model. Through coordinate transformation law, the uniaxial failure stresses were then converted to a plot of shear stress versus transverse normal stress from which the shear strength in the absence of transverse normal stress ( σ 22 = 0) was obtained. Experimental results showed that the shear strength of the composite is quite sensitive to strain rate and the shear strength increases as strain rate increases. In contrast, the shear failure strain decreases as strain rate increases.

A strain rate dependent constitutive model for clays at residual strength

Plasticity theory is extended to incorporate strain rate effects on the residual shear strength of clays. The clay is assumed to behave elastically before yielding and then in a perfectly plastic manner with no volume change during yielding. The Mohr-Coulomb failure criterion is used in the rate-dependent model in which the strain rate affects the mobilized effective friction angle of the material. During initial yielding and subsequent plastic deformation, the stress and strain states at a point will satisfy the rate-dependent yield function (loading function). When the effective plastic strain rate decreases to a threshold strain value, the loading surface moves, or collapses, to the static yield surface. A constant volume flow rule is used to calculate plastic deformation. The computed stress-strain relationship is formulated in two parts, namely a rate-independent part and a rate-dependent part. The rate-independent part is the same as that used in classical elastoplastic formulations, whereas the rate-dependent part is dependent on the current strain rate of the material. The use of the model is illustrated using a numerical example simulating a two-dimensional plane strain test.Key words: constitutive relationship, finite element, plasticity theory, pre-sheared clay, rate effects, residual strength.

Adiabatic shear bands in axisymmetric impact and penetration problems

We study axisymmetric deformations of depleted uranium (DU) and tungsten heavy alloy (WHA) rods impacting at normal incidence either a flat rigid or a thick steel target. Each deformable material is modeled as elastic thermoviscoplastic; its flow stress increases with an increase in the effective plastic strain and effective plastic strain-rate but decreases with a rise in the temperature. An objective of this work is to ascertain when and where a shear band, defined as a narrow region of rapid, intense plastic deformation, forms in each material. The Taylor impact simulations show that shear bands form earlier in WHA than in DU for material parameters used. In the penetration simulations, shear bands form continuously in the ejecta of the DU penetrator but only one shear band occurs in the WHA ejecta followed by its more uniform deformations.

Effect of strain rate on nonlinear deformation behavior in CFRP composites

This paper presents the effect of strain rates on nonlinear deformation behavior of CFRP composites. An elastic-plastic constitutive model is developed on the basis of both a complementary elastic energy function and a plastic potential, assuming that linear elastic deformation occurs in the fiber direction and that nonlinear strain in the shear direction is decomposed into nonlinear elastic strain and plastic strain. A one-parameter and a two-parameter plastic potential are employed to describe post-yielding behavior of composite laminae. Nonlinear elastic shear strain is measured by means of loading/unloading tensile tests of [±45°]s specimens. Off-axis tensile tests are performed to obtain the universal effective stress-effective plastic strain relation under monotonic loading. It is shown that rate-dependence of effective stress-effective plastic strain relation can be explained by determining anisotropy parameters of the plastic potential as functions of initial effective plastic strain rate.

Ductile damage and fracture finite element modelling of elasto-viscoplastic voided materials

Micro-structure void volume fraction is taken into account with finite element models developed for high strain rate elasto-viscoplastic problems. Void nucleation rate depends on matrix effective strain rate, void growth on material strain rate and elasto-viscoplastic potential proposed for porous material, void coalescence on matrix effective plastic strain rate and ductile fracture on critical void volume fraction. A radial return algorithm is proposed for the implementation into explicit finite element frameworks. Reference finite element modelling of ductile damage increases and fracture occurrence is performed for high-speed upsetting of steel multi-tubular.