Numerical modeling of response of monolithic and bilayer plates to impulsive loads

In this paper, we present and discuss the results of our numerical simulation of the dynamic response and failure modes of circular DH-36 steel plates and DH-36 steel–polyurea bilayers, subjected to impulsive loads in reverse ballistic experiments. In our previous article, we reported the procedure and results of these experiments [MR Amini, JB Isaacs, S Nemat-Nasser. Experimental investigation of response of monolithic and bilayer plates to impulsive loads. accepted]. For the numerical simulations, we have used physics-based and experimentally-supported temperature- and rate-sensitive constitutive models for steel and polyurea, including in the latter case the pressure effects. Comparing the simulation and the experimental results, we focus on identifying the potential underpinning mechanisms that control the deformation and failure modes of both monolithic steel and steel–polyurea bilayer plates.The numerical simulations reveal that the bilayer plate has a superior performance over the monolithic plate if the polyurea layer is cast on its back face (opposite to the blast-receiving side). The presence of the polyurea layer onto the front face (blast-receiving side) amplifies the initial shock loading and thereby enhances the destructive effect of the blast, promoting (rather than mitigating) the failure of the steel plate. In addition, the interface bonding strength between polyurea and steel is examined numerically and it is observed that the interface bonding strength has a significant effect on the performance of the steel–polyurea bilayer plates. The numerical simulations support the experimentally observed facts provided the entire experiment is simulated, employing realistic physics-based constitutive models for all constituents.     

An approximating model of failure of structural materials and a problem of a failure wave

A method of numerical calculation of a failure wave in a brittle material in pulsed loading is proposed. The method is based on the variation of the elasticity modulus in transition through the wave front. The results of calculating the movement of a spherical failure wave are presented.Translated from Problemy Prochnosti, No. 9, pp. 4–6, September, 1991.     

Strength and Failure Modes of Hoop Wound CFRP Tubes Under Compressive High Rates of Loading

A study was undertaken to investigate the response of hoop wound carbon fibre reinforced plastic (CFRP) tubes to dynamic compressive loading at strain rates in the range of 5–200/sec. An experimental rig was designed and built to test short tubular specimens under external radial pressure with minimum end constraints. The load was applied by detonating a small explosive charge inside a water filled, steel, cylindrical chamber enclosing the test specimen. For each test the external pressure and the strains, in both circumferential and longitudinal directions, were recorded on suitable digital processing equipment. Two distinct modes of failure were identified; material and structural (buckling). The mode of failure was dependent on the rate of loading and the tube diameter/thickness ratio. For 100 mm diameter tubes with diameter/thickness=40, buckling failure dominated at strain rates below 10/s. However, at higher strain rates, material failure and a considerable enhancement in burst strength was observed. For 100 mm diameter tubes, with diameter/thickness=80, a buckling mode of failure was in evidence in all the tests, irrespective of the rate of loading.R. Ahmad: Presently at School of Mechanical Engineering, University Sains Malaysia, Pulau Pinang, Malaysia.     

Consideration of defects in calculating the failure probability of ceramic articles with short-term loading

On the basis of analyzing current approaches it is concluded that the optimum approach to estimating the failure probability for ceramic articles with short-term loading should be a combination of explicit and implicit consideration of different features of material defects and the stressed state. Calculation dependences developed by the authors are given in explicit form which consider separately the effect of surface and volume defects, the form of stressed state, curvature of the loading path, and the nature of defect orientation distribution. The effect of loading path curvature on the calculated failure probability is demonstrated by a numerical example. Methods are considered for determining the parameters of material surface and volume defects used in the suggested relationships.Translated from Problemy Pochnosti, No. 4, pp. 25–30. April, 1991.     

Fatigue properties of jointed wood composites Part II Life prediction analysis for variable amplitude loading

A method of predicting lifetime to failure for any wood composite system subjected to a complex load–time history has been developed. The prediction first requires the generation of a simple model to characterize the fatigue response of the particular composite system and a rainflow analysis breakdown of the load–time history under investigation. Once the models are derived they can be used to predict lifetimes to failure for any load–time history using a modified Palmgren–Miner damage summation rule. Variable amplitude fatigue testing of sample material using the same load–time histories allowed a comparison to be made between predicted and actual lifetimes to failure and was useful in verifying and refining the life prediction models. © 1998 Kluwer Academic Publishers     

Prediction of Critical Properties of Mixtures from the PRSV-2 Equation of State: A Correction for Predicted Critical Volumes

The predictive capability of the Peng–Robinson–Stryjek–Vera (PRSV-2) equation of state (1986) for critical properties of binary mixtures was investigated. The procedure adopted by Heidemann and Khalil (1980) and discussed by Abu-Eishah et al. (1998) was followed. An optimized value for the binary interaction parameter based on minimization of error between experimental and predicted critical temperatures was used. The standard and the average of the absolute relative deviations in critical properties are included. The predicted critical temperature and pressure for several nonpolar and polar systems agree well with experimental data and are always better than those predicted by the group-contribution method. A correction is introduced here to modify the predicted critical volume by the PRSV-2 equation of state, which makes the average deviations between predicted and experimental values very close to or even better than those predicted by the group-contribution method.     

Deformation and tearing of blast-loaded stiffened square plates

Experimental and numerical results for fully built-in stiffened square plates subjected to blast pressure loading are presented. The strain rate-sensitive plates exhibit mode I (large ductile deformation) and mode II (tensile tearing) failure as the load intensity increases. The numerical analysis is carried out using a finite element formulation which incorporates non-linear geometry and material effects as well as strain rate sensitivity. Mode I is predicted well for both maximum deflection and deformation shape. Initiation of mode II failure is predicted by a maximum strain criterion, but the limited mode II data is insufficient for conformation.     

Method of investigating nonaxisymmetric dynamic form change in failing shells. Report 1. Theory and numerical method

A mathematical theory describing processes of vigorous dynamic form change in elastoplastic nonaxisymmetric shells is proposed. The damage sustained by the material right up to failure is considered. An analytical method of calculating the nonstationary load on a shell is presented for the case of a hydrodynamic loading. A numerical integrointerpolation method of solving the indicated initially boundary nonlinear nonstationary problem is developed.Translated from Problemy Prochnosti, No. 3, pp. 5–19, March, 1996.     

Fracture and progressive failure of defective graphene sheets and carbon nanotubes

An atomistic based finite bond element model for the prediction of fracture and progressive failure of graphene sheets and carbon nanotubes is developed by incorporating the modified Morse potential. The element formulation includes eight degrees of freedom reducing computational cost compared to the 12 degrees of freedom used in other FE type models. The coefficients of the elements are determined based on the analytical molecular structural mechanics model developed by the authors. The model is capable of predicting the mechanical properties (Young’s moduli, Poisson’s ratios and force–strain relationships) of both defect-free and defective carbon nanotubes under different loading conditions. In particular our approach is shown to more accurately predict Poisson’s ratio. The numerical prediction of nonlinear stress–strain relationships for defect-free nanotubes including ultimate strength and strain to failure of nanotubes is identical to our analytical molecular structural mechanics solution. An interaction based mechanics approach is introduced to model the formation of Stone–Wales (5-7-7-5) topological defect. The predicted formation energy is compared with ab initio calculations. The progressive failure of defective graphene sheets and nanotubes containing a 5-7-7-5 defect is studied, and the degradation of Young’s moduli, ultimate strength and failure strains of defective nanotubes is predicted.     

Nonlinear shear properties of spruce softwood: Numerical analyses of experimental results

Determination of material parameters from experimental tests often rely on simplifying assumptions like the existence of uniform stress and strain fields within the considered part of the test specimen. However, more detailed analyses usually show that the stress and strain fields differ from the assumed (nominal) uniform distributions. In order to utilize the potential of numerical analyses of wooden structures by the FEM method, the nominal material parameters measured directly from tests need to be re-evaluated in order to make them more useful for FEM models and to make FEM models more reliable.Experimental data from shear testing of clear wood from Norway spruce was analysed numerically with a bilinear material law in shear. The inherent material parameters were fitted to the experimental behaviour by means of optimization methods in conjunction with FEM analyses. The study included six Arcan test configurations comprising the three orthotropic material planes of wood, and covered the whole loading range until failure. Compared to numerical results, it was found that stiffness values measured were too high, and that downward adjustments in the range of 5–30% were required. Linear limit stresses between 40% and 60% of the nominal shear strengths were found, whilst the tangent moduli ranged between 30% and 70% of the linear elastic shear moduli. The rolling shear plane RT showed most nonlinearity and the LT plane least. Analyses with modified bilinear parameters showed good correspondence with experimental findings. The parameters were found to be relatively well adapted by Weibull distributions.     

Numerical investigation of the dynamic strength of thick-walled cylindrical shells with cracklike technological defects

A numerical method is proposed for the evaluation of the stress intensity factors in elastic thick-walled cylindrical shells with cracks subjected to dynamic loading. The method is based on the two-dimensional axially symmetric Wilkins algorithm and the equations of mechanics of brittle fracture. The strength of thick-walled cylinders loaded by pulses of internal pressure and containing technological defects (similar to mathematical cuts) formed at the sites of fixing of their ends by welding is investigated.Translated from Problemy Prochnosti, No. 1, pp. 76–87, January–February, 2005.     

Energy absorption and ductile failure in metal sheets under lateral indentation by a sphere

This paper is concerned with the mechanics of lateral indentation of a rigid sphere into a thin, ductile metal plate. The paper presents a study including experiments, analytical theories and finite element calculations. The focus is on the prediction plate failure and on the energy absorption up to this point. Load–displacement curves from experiments are presented for various plate geometries (circular, square, rectangular), indentor radii and locations of loading on the plate. The experiments show that the penetration to ductile fracture and the energy absorption is sensitive to both plate geometry, loading position and indentor geometry. The plate fails by localised necking followed closely by material fracture. Analytical theories are derived for the load–displacement behaviour of a plastic membrane up to failure. The point of plate failure is determined by a global stability criterion taking into account both the change of geometric and material stiffness during the indentation process. For the cases of axis-symmetric loading very good agreement between measured and theoretical load–displacement curves up to — and including — the point of initial plate failure is found. Curve fitting to the theoretical solutions produced the following expressions for the penetration and absorbed energy up to plate failure: where C₀ and n are the strength coefficient and the hardening exponent in the material power law, t₀ is the initial plate thickness, R_b is the indentor radius and R is the plate radius. The tests were also modelled by the use of a commercially available finite element program. It is shown that the applied finite element method can accurately predict the response up to necking and fracture initiation for both symmetric and non-symmetric loading.     

Anisotropic ductile failure in free machining steel at quasi-static and high strain rates

Leaded Free Machining Steel (FMS) specimens were tested in tension at quasi-static and high strain rates in both the longitudinal and transverse directions with respect to the axis of the bar material. For the quasi-static tests, a high degree of anisotropy of fracture behaviour was observed for both plain (unnotched) and notched specimens. However the difference in fracture strains for longitudinal and transverse directions was significantly reduced for the high stress triaxiality conditions produced by the sharper notches. Plain specimens tested at dynamic strain rates (10³ s⁻¹) failed at somewhat higher strains than those tested quasi-statically. For the notched specimens tested dynamically, there was a transition to a brittle mode of failure and there was no statistically significant anisotropy in the very low strains to failure recorded. These experimental results were linked to numerical predictions of the local stress, strain and strain rate conditions in the specimens carried out using a modified Armstrong–Zerilli constitutive model for the FMS. Changes in the percentage area and aspect ratio of the lead inclusions which act as sites for void growth under ductile failure conditions were measured for both longitudinal and transverse directions of loading. It was found that the apparent area of inclusions increases with degree of deformation due to void growth but that the aspect ratio decreases due to the inclusions/voids becoming more spherical. This effect was greater for loading in the transverse direction indicating that voids grow more readily from inclusions when the latter are aligned perpendicular to the direction of loading.     

A numerical investigation of the failure of spherical shells in explosive loading

The results of numerical simulation of the deformation and failure of spherical shells in explosive loading are presented. The known criteria of failure of materials in dynamic loading are analyzed and the desirability of their use is shown. A comparison is made of the numerical results obtained and experimental data.Translated from Probblemy Prochnosti, No. 8, pp. 9–14, August, 1992.     

Examination of the failure of sandwich beams with core junctions subjected to in-plane tensile loading

The paper concerns local effects occurring in the vicinity of junctions between different cores in sandwich beams subjected to tensile in-plane loading. It is known from analytical and numerical modelling that these effects display themselves by an increase of the bending stresses in the faces as well as the core shear and transverse normal stresses at the junction. The local effects have been studied experimentally to assess the influence on the failure behaviour both under quasi-static and fatigue loading conditions. Typical sandwich beam configurations with aluminium and glass-fibre reinforced plastic (GFRP) face sheets and core junctions between polymer foams of different densities and rigid plywood or aluminium were investigated. Depending on the material configuration of the sandwich beam, premature failure accumulating at the core junction was observed for quasi-static and/or fatigue loading conditions. Using Aluminium face sheets, quasi-static loading caused failure at the core junction, whereas no significance of the junction was observed for fatigue loading. Using GFRP faces, a shift of the failure mode from premature core failure in quasi-static tests to face failure at the core junction in fatigue tests was observed. In addition to the failure tests, the sandwich configurations have been analysed using finite element modelling (FEM) to elaborate on the experimental results with respect to failure prediction. Both linear modelling and nonlinear modelling including nonlinear material behaviour (plasticity) was used. Comparing the results from finite element modelling with the failure behaviour observed in the quasi-static tests, it was found that a combination of linear finite element modelling and a point stress criterion to evaluate the stresses at the core junction can be used for brittle core material constituents. However, this is generally not sufficient to predict the failure modes and failure loads properly. Using nonlinear material properties in the modelling and a point strain criterion improves the failure prediction especially for ductile materials, but this has to be examined further along with other failure criteria.     

Analysis of the interaction of adjacent layers of a GFRP-laminate under fatigue loading

A layer-wise strength analysis of laminates leads to realistic results not only with quasistatic but also with cyclic loading. The used fatigue strength has to be determined by experiment. Degradation models exist, used to reduce the laminate stiffness due to inter-fibre fracture (IFF) cracks. However a notch effect caused by IFF – in other words, a local increase in stress in the laminate adjacent to the laminate affected by an IFF – is not included. This leads to a premature failure of the laminate much earlier as it is predicted by a failure criteria. Performing 3-point-bending tests the notch effect was measured to obtain a more exact service life prediction. Adequate crack arresting layers are tested which will reduce the negative notch effect.     

Nucleation and growth of a macrocrack in tension and compression

Conclusions The general approach to analysis of the processes of nucleation and growth of radial separation macrocracks from the surface of a circular hole in sheets deformed in tension and compression was used to obtain new relations for calculating the characteristic values of compressive and tensile loads. The calculated results are in satisfactory agreement with the results of tests on sheets. At the same time, we detected unexpected fundamentally important aspects of the problem of brittle failure by separation.Firstly, it is justified to assume that the length of the region of the strong effect of the free surface of the hole on the state of the zone of development of the failure process in compression can be an order of magnitude higher than that in tensile loading. Secondly, with an increase of the distance of the crack tips from the hole the resistance of the material to failure in compressive loading gradually increases from the value close to minimum, at which k = 0, to its maximum value at k=-. If both these claims are valid, in future it would be necessary to revise greatly the methodology, results, and conclusions of a large number of investigations of brittle failure in compression, partially, in tension.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 27, No. 5, pp. 62–66, September–October, 1991.     

Method of investigating the nonaxisymmetric dynamic form changing of collapsible shells. Report 2. Calculations and experiment

The theory and numerical method of calculating the significant nonstationary form change of nonaxisymmetric elastoplastic shells with allowance for material failure are confirmed. The confirmation is based on numerical experimentation, and comparison of numerical results with test calculations and experimental data. Satisfactory accuracy is noted for this numerical method and the computational results obtained. Some characteristic features of the dynamic failure of the shells are disclosed.Translated from Problemy Prochnosti, No. 4, pp. 41–48, April, 1996.     

An experimental and numerical study of the effects of length scale and strain state on the necking and fracture behaviours in sheet metals

Within sheet metal forming, crashworthiness analysis in the automotive industry and ship research on collision and grounding, modelling of the material failure/fracture, including the behaviour at large plastic deformations, is critical for accurate failure predictions. In order to validate existing failure models used in finite element (FE) simulations in terms of dependence on length scale and strain state, tests recorded with the optical strain measuring system ARAMIS have been conducted. With this system, the stress–strain behaviour of uniaxial tensile tests was examined locally, and from this information true stress–strain relations were calculated on different length scales across the necking region. Forming limit tests were conducted to study the multiaxial failure behaviour of the material in terms of necking and fracture. The failure criteria that were verified against the tests were chosen among those available in the FE software Abaqus and the Bressan–Williams–Hill (BWH) criterion proposed by Alsos et al, 2008. The experimental and numerical results from the tensile tests confirmed that Barba's relation is valid for handling stress–strain dependence on the length scale used for strain evaluation after necking. Also, the evolution of damage in the FE simulations was related to the processes ultimately leading to initiation and propagation of a macroscopic crack in the final phase of the tensile tests. Furthermore, numerical simulations using the BWH criterion for prediction of instability at the necking point showed good agreement with the forming limit test results. The effect of pre-straining in the forming limit tests and the FE simulations of them is discussed.