Response of titanium alloys to high strain rate deformation

Abstract

The stress-strain response of samples of Ti64 and Ti550 at strain rates from 10^?1 s^?1 to 10³ s^?1 and samples of Ti811 and Ti153 at a strain rate of 10³ s^?1 have been assessed. It has been found that the influence of the imposed strain rate on the stress-strain response of Ti64 and Ti550 alloys is very similar – in both alloys the yield stress increases with increase of strain rate and the energy absorbed to fracture increases. At high strain rates localised deformation occurs in the form of shear bands in Ti64 and Ti550 but no shear banding was seen in Ti811 and Ti153. The fracture surfaces of Ti64 and of Ti550 show an increased tendency to brittle failure and an increase in necking with increase of strain rate. The influence of alloy microstructure and composition on the response to changes in imposed strain rate are discussed in terms of adiabatic heating and the factors controlling the flow stress in these alloys.     

Strength,deformation, fracture behaviour and ductility of aluminium-lithium alloys

The ever increasing need for high strength, improved performance, lightweight and cost-effective materials has resulted in significant improvements and development of new aluminium alloys for structural applications. Lithium additions to aluminium have the potential for providing a class of high strength alloys with exceptional properties suitable for weight-critical applications. In this paper, published studies of composition-processing-microstructure relationships are discussed. Contributions to strength of the solid solution are discussed with reference to the presence of lithium in solid solution, the presence of coherent, ordered precipitates in the matrix and the co-precipitation of binary, ternary and more complex strengthening phases. Microstructural influences on strength are discussed with reference to metallurgical variables. These variables include the intrinsic microstructural features; the presence of dispersoids, the nature and type of matrix strengthening precipitates and the presence of denuded zones adjacent to grain boundaries. The extrinsic and intrinsic micromechanisms governing the deformation characteristics and fracture behaviour are critically examined with specific reference to ageing condition of the alloy, the matrix slip characteristics, and the nature, volume fraction and distribution of strengthening precipitates. The deleterious effects of strain localization and the exacerbating effect of precipitate-free zones are also highlighted. The micromechanics governing the fracture processes are examined and the sequence of events in the fracture process is reviewed in light of the specific role of several concurrent factors involving nature and volume fraction of second-phase particles, deformation mode, and dislocation-microstructure interactions. Past attempts made to improve the tensile ductility and mechanical response of these alloys are also examined so as to provide a better basis for understanding processing-microstructure-deformation interactions.     

Ductile fracture mechanism of low-temperature In-48Sn alloy joint under high strain rate loading

The failure behaviors of In-48Sn solder ball joints under various strain rate loadings were investigated with both experimental and finite element modeling study. The bonding force of In-48Sn solder on an Ni plated Cu pad increased with increasing shear speed, mainly due to the high strain-rate sensitivity of the solder alloy. In contrast to the cases of Sn-based Pb-free solder joints, the transition of the fracture mode from a ductile mode to a brittle mode was not observed in this solder joint system due to the soft nature of the In-48Sn alloy. This result is discussed in terms of the relationship between the strain-rate of the solder alloy, the work-hardening effect and the resulting stress concentration at the interfacial regions.     

Texture evolution and dynamic mechanical behavior of cast AZ magnesium alloys under high strain rate compressive loading

In this study, texture and compressive mechanical behavior of three cast magnesium alloys, including AZ31, AZ61 and AZ91, were examined over a range of strain rates between 1000 and 1400 s⁻¹ using Split Hopkinson Pressure Bar. Texture measurements showed that after shock loading, initial weak texture of the cast samples transformed to a relatively strong (00.2) basal texture that can be ascribed to deformation by twinning. Furthermore, increasing the aluminum content in the alloys resulted in increase in the volume fraction of β-Mg₁₇Al₁₂ and Al₄Mn phases, strength and strain hardening but ductility decreased at all strain rates. Besides, it was found for each alloy that the tensile strength and total ductility increased with strain rate. By increasing the strain rate, the maximum value of strain hardening rate occurred at higher strains. Also, it is suggested that a combination of twinning and second phase formation would affect the hardening behavior of the cast AZ magnesium alloys studied in this research.     

Ultra high molecular weight polyethylene deformation and fracture behaviour as a function of high strain rate and triaxial state of stress

The dynamic response and fracture characteristics of Ultra High Molecular Weight Polyethylene (UHMWPE) were investigated both experimentally and numerically. The strain rate sensitivity of the material was studied by carrying out tensile tests on smooth cylindrical specimens over a range of high strain rate conditions using the purpose built `flying wedge' testing machine at separation velocities up to 9 m/s. The effect of the initial stress triaxiality conditions on the material's ductility at different strain rates was studied using pre-notched cylindrical specimens with different notch radii. The true stress-strain results indicated that the tested material is highly sensitive to strain rate changes. Post-fracture geometric measurements of the fractured specimens indicated that the ductility of UHMWPE is strongly dependent on both the initial stress triaxiality conditions and the strain rate. Numerical simulations of the quasi-static and high strain rate tests were used to predict, for different notch radii, variation of the centre-most element radial strain and stress triaxiality factor with the average radial strain. Based on the combined numerical and experimental results, a simple relation for the ductile fracture of UHMWPE was derived as a function of stress triaxiality and strain rate.     

Material deformation and fracture under impulsive loading conditions

Engineering structures experience impulsive loads during the time of natural disasters like earthquakes, cyclones and collisions. The design of structures resistant to such natural disasters requires an understanding of the deformation and fracture behaviour of the materials constituting the structure under impulsive loading conditions. In this paper the various aspects of dynamic plastic deformation and fracture of common engineering materials are reviewed and contrasted with their behaviour under static loading conditions.     

Failure analysis of quasi-isotropic CFRP laminates under high strain rate compression loading

Dynamic compressive strength of quasi-isotropic fiber composite is investigated experimentally and also numerically simulated. In-plane compression tests at strain rates around 400/s quasi-isotropic laminates were performed using the Split Hopkinson Pressure Bar (SHPB). The material system used was Texipreg^® HS160 REM, comprising high strength unidirectional carbon fiber and epoxy resin. The dynamic strength of quasi-isotropic laminates exhibits a considerable increase when compared to the static values. The finite-element model used ABAQUS™ three-dimensional solid elements C3D8I with 8 nodes and user-defined interface finite elements with 8 nodes [Gonçalves JPM, de Moura MFSF, de Castro PMST, Marques AT. Interface element including point-to-surface constraints for three-dimensional problems with damage propagation. Eng Comp: Int J Comput Aided Eng Software 2000;17(1):28–47; de Moura MFSF, Pereira AB, de Morais AB. Influence of intralaminar cracking on the apparent interlaminar mode I fracture toughness of cross-ply laminates. Fatigue Fract Eng Mater Struct 2004;27(9):759–66.]. These interface elements which connect the three-dimensional solid elements modeling the composite layers, include a cohesive damage model allowing the simulation of delamination initiation and propagation. Hence the present model assumes that the phenomenon of failure under these conditions is mainly dictated by interface delamination. This is supported by experimental tests which showed that all quasi-isotropic laminates split into several almost intact sublaminates. The model compares very well with experimental results, confirming the formulated hypothesis that the internal layer damage does not markedly contribute to the quasi-isotropic laminate failure.     

Impact behavior and constitutive model of nanocrystalline Ni under high strain rate loading

To investigate mechanical properties and deformation mechanisms of nanocrystalline materials under high strain rate, dynamic impact tests for nanocrystalline Ni bulk prepared by high-energy ball milling combined with compaction and hot-pressure sintering were carried out under different high strain rates on Split Hopkinson bar. Compared with the testing results under quasi-static strain rate, the nanocrystalline Ni has higher strength under high strain rate. Meanwhile, the impact stress–strain curves exhibit rate-dependence strength and light strain hardening behavior. Subsequently, a mechanism of dislocation gliding in combination of grain boundary sliding was discussed and a constitutive model was built under high strain rate loading based on the mechanism. The predictions of the constitutive model under high strain rates show good agreements with the experimental data. Finally, the properties of the nanocrystalline Ni were discussed in detail.     

The effects of bond thickness, rate and temperature on the deformation and fracture of structural adhesives under shear loading

The deformation and fracture in shear of a structural adhesive undergoing large-scale yielding is studied as a function of bond thickness, h, temperature, T, and strain rate using the Napkin Ring specimen. The lack of edges in this test, and the fact that the strain rate can be locally controlled, allow for a meaningful evaluation of the mechanical response throughout the deformation process. In accord with Airing's molecular activation model, the yield stress linearly decreases with T while logarithmically increasing with the strain rate. The ultimate shear strain, _F, is little sensitive to rate while decreasing with h and increasing with T. Some complementary fracture tests are carried out using the ENF bond specimen in order to explore the relation between the mechanical properties of the nominally unflawed adhesive and the mode II fracture energy, G _IIC. For sufficiently thin bonds, G _IIC/h correlates well with the ultimate energy density (i.e., the area under the stress-strain curve in the Napkin Ring test), given, to a first approximation, by _YF, where _Y is the yield stress in shear. Accordingly, the fracture energy of the bond would be greatly affected by temperature, tending to a small value at the absolute as well as the glass transition temperatures while attaining a maximum in between these two extremes. Because the yield stress does not vary much with h, the variation of G _IIC with the bond thickness reflects that of _F.A large-deformation fracture analysis, based on a cohesive zone like model, is developed to account for the observed variations of _F with h. The analysis assumes that a crack preexist in the bond, either at its center or at the interface. The results suggest that the observed increase of _F with decreasing h is due mainly to two geometric effects. The first is due to the interaction of the bonding surfaces with the stress field generated by the crack and the second has to do with the probability of finding large flaws in the bond to trigger the fracture.     

Effect of strain rate on the fracture behaviour of collagen

The strain-rate dependence of collagen fibre, a viscoelastic material, was studied both in the native and dry conditions. The strain rate effect was observed in the stress-strain, plastic set behaviour of both dry and wet collagen fibres. Fractured ends of the broken fibres, observed using scanning electron microscopy, showed that the fracture behaviour was different at high and low strain rates. The results are compared with those for elastoidin.     

Effect of strain rate on tensile deformation and fracture behaviour of 18%Ni 300 maraging steel sheet

Abstract

Deformation and fracture under uniaxial tensile loading at room temperature were investigated for 18%Ni 300 maraging steel sheet in the strain rate range 1·67×10^?5 to 1·67× 10^?1s^?1. The steel showed an increase in flow stress with strain rate and the increase in yield strength (YS) was more pronounced compared with the tensile strength (TS), resulting in a corresponding decrease of TS/YS ratio. Both the level of deformation and the deformation zone were also reduced by the increasing strain rate. Fractographic analysis indicated that the increasing strain rate induced, to some extent, plane strain constraint in the sheet resulting in increasing fracture angle, decreasing ductility/fracture strain, and increasing dimple size. With increasing strain rate the work hardening rate dσ/d? and strain hardening coefficient (n value) of the steel also decreased; hence, correlations were found between dσ/d?, TS/YS ratio, and n value. The decrease of these three parameters caused strain localisation as confirmed by the presence of intergranular dimples and intergranular shear. Also, the dimple density decreased as the strain rate was increased.

MST/729     

Dynamic expansion modeling of a thick-walled cylinder under internal high strain rate loading

This article presents analysis of the dynamic behavior of a thick-walled cylinder under the assumption of nonlinear strain rate hardening behavior under high strain rate loading before any fracture on the surface. The theoretical model applies both to direct and indirect use of dynamic strength of material and instant boundary conditions to establish a differential equation for radial expansion velocity. Further, detailed discussion will be given with emphasis on the main aspects of the cylinder behavior, i.e., radial displacement, internal pressure, strain rate, flow stress, radial and tangential stress, and the influence of the different material rate sensitive exponent.     

Impact and fracture response of sintered 316L stainless steel subjected to high strain rate loading

This paper describes the use of a material testing system (MTS) and a compressive split-Hopkinson bar to investigate the impact behaviour of sintered 316L stainless steel at strain rates ranging from 10^− 3 s^− 1 to 7.5 × 10³ s^− 1. It is found that the flow stress–strain response of the sintered 316L stainless steel depends strongly on the applied strain rate. The rate of work hardening and the strain rate sensitivity change significantly as the strain rate increases. The flow behaviour of the sintered 316L stainless steel can be accurately predicted using a constitutive law based on Gurson's yield criterion and the flow rule of Khan, Huang and Liang (KHL). Microstructural observations reveal that the degree of localized grain deformation increases at higher strain rates. However, the pore density and the grain size vary as a reversible function of the strain rate. Impacts at strain rates higher than 5.6 × 10³ s^− 1 are found to induce adiabatic shear bands in the specimens. These specimens subsequently fail as a result of crack propagation along the dominant band. The fracture surfaces of the failed specimens are characterized by dimple-like structures, which are indicative of ductile failure. The depth and the density of these dimples are found to decrease with increasing strain rate. This observation indicates a reduction in the fracture resistance and is consistent with the observed macroscopic flow stress–strain response.     

Dynamic compressive behaviour of Ti-6Al-4V alloy processed by electron beam melting under high strain rate loading

This paper documents an investigation into the compressive deformation behaviour of electron beam melting(EBM) processing titanium alloy(Ti-6A1-4V) parts under high strain loading conditions.The dynamic compression tests were carried out at a high strain rate of over1×10~3/s using the split Hopkinson pressure bar(SHPB)test system and for comparison the quasi-static tests were performed at a low strain rate of 1×10~3/s using a numerically controlled hydraulic materials test system(MTS) testing machine at an ambient temperature.Furthermore,microstructure analysis was carried out to study the failure mechanisms on the deformed samples.The Vickers micro-hardness values of the samples were measured before and after the compression tests.The microstructures of the compressed samples were also characterized using optical microscopy.The particle size distribution and chemical composition of powder material,which might affect the mechanical properties of the specimens,were investigated.In addition,the numerical simulation using commercial explicit finite element software was employed to verify the experimental results from SHPB test system.     

Comparisons of deformation and fracture behaviour of PC/ABS blend and ABS copolymer under dynamic shear loading

Abstract

The dynamic shear deformation and fracture characteristics of PC/ABS blend and ABS copolymer with regard to the relation between mechanical properties and strain rate, are studied experimentally using a torsional split Hopkinson bar at room temperature under strain rates ranging from 8 × 10² s^-1 to 3.4 × 10³ s^-1. Fracture phenomena are analysed by scanning electron microscopy and correlated with macroscopic behaviour. The relative properties and fracture mechanism of both polymers are also compared. Results show that strain rate enhances shear strength of both PC/ABS blend and ABS, but fracture shear strain tends to decrease with increasing strain rate. ABS exhibits better ductility and lower shear strength. For both polymers, strain rate sensitivity increases with increasing range of strain rate, while an inverse tendency occurs for activation volume. Higher strain rate sensitivity and lower activation volume are found in PC/ABS blend. PC/ABS blend fracture is dominated by mixed shearing and tearing, but ABS fracture shows only shearing. Due to the increasing deformation heat, fracture surface viscoplastic flow for both polymers increases with increasing strain rate, inducing lower flow resistance and lower fracture strain at higher stain rates. The viscoplastic flow behaviour in ABS is more active.     

Modeling of dynamic expansion of thick‐walled cylinder under high strain rate loading with strain rate sensitivity analysis

This paper presents an analysis of the dynamic behavior of thick‐walled cylinder using Levy‐Mises flow rule in the assumption of a non‐linear strain rate hardening behavior under high strain rate loading. The theoretical model to be developed in this work applies indirect use of dynamic strength of material characterized by a non‐linear relation and instant boundary condition based on Jones‐Wilkins‐Lee equation of state to establish differential equation for radial expansion velocity. Detailed discussion will be given with emphasis on the main aspects of the cylinder behaviour, i.e. radial displacement, internal pressure, strain rate, flow stress, radial and tangential stress and the influence of different material rate sensitive exponent. Results show a good agreement with the analytical solutions proposed here.     

Modeling of structures subjected to impact: concrete behaviour under high strain rate

This paper deals with a viscoplastic model which is the natural way to take into account the rate effect. Consideration of viscosity averts the habitual mesh sensitivity when strain softening is introduced by preserving the well-posedness of the initial boundary value problem. Modeling can constitute an alternative to experimentation not in order to predict the material response, but to try to understand and to evaluate the rate effect. Numerical simulation of the split test Hopkinson pressure bar gives an idea of dynamic concrete behaviour: forces of inertia, inertial confinement, structural effect and rate effect. Finally, the model is used to simulate a reinforced concrete beam submitted to impact.