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.     

Development of de-alloyed zones during oxidation: effects on microstructure and spallation behaviour

Abstract

The development of de-alloyed zones during oxidation of martensitic and austenitic steels and Ni based superalloys has been reviewed and the influence of de-alloying on local creep strength has been assessed. The de-alloyed zones in martensitic steels have similar, possibly higher, strength than the bulk material, whereas in Ni based superalloys the de-alloyed zone is significantly weaker than the bulk alloy. The effect in austenitic steels varies according to the strengthening phases present in the alloys: the de-alloyed zone is weaker in alloys strengthened by chromium carbides and/or γ′ but has similar strength in alloys strengthened by niobium carbide.     

High strain rate induced initial chip formation of certain metals during micromachining processes

Abstract

As microtechnology and nanotechnology become increasingly important to the needs of society, the need to create devices in engineering materials becomes more apparent. High speed milling has been shown to provide a great deal of promise in creating microstructures and in nanotexturing surfaces in engineering materials. Cutting tool rotation is expected to reach 1 000 000 revolutions per minute (rev min^?1) compared with conventional cutting speeds of around 30 000 rev min^?1. Rotating the tool this quickly reduces cutting forces, which produces a higher quality of cut so that post- processing is not required. Clearly, strain rates imparted to the workpiece at these speeds are very high and this influences initial chip formation and chip removal mechanisms. High strain rates imparted cause distinct chip formations in engineering materials to occur which are similarly observed in other materials, most notably biological materials such as cancellous bone. Certain soft metals such as aluminium do not machine very well because the material adheres to the cutting tool. However, high strain rates tend to overcome these limitations. This paper examines high strain rate initial chip formation in metals, compares these results to other materials, and shows that an initial chip curl model can be applied to describe high strain rate machining phenomena at the microscale.     

Effect of variation of strain rate on thermal and acoustic emission during tensile deformation of nuclear grade AISI type 316 stainless steel

Abstract

A systematic study has been undertaken to correlate the changes in thermal and acoustic emissions during tensile deformation of AISI type 316 nuclear grade stainless steel (SS) due to variations in the strain rate. Strain rates were varied in the range 3.3 × 10^-4s^-1 to 1.7 × 10^-2s^-1. Thermal emissions were monitored using a focal plane array based thermal imaging system. For a given strain rate, the rate of increase in temperature was observed to be gradual and uniform in the work hardening zone, and to increases drastically during necking. With increasing strain rate, the temperature also increased. Based on the experimental results a constitutive equation can be modelled relating the rise in temperature to strain rate. In the case of acoustic emission (AE), the root mean square (RMS) voltage of the AE signal and cumulative counts increase with strain rate due to the increase in source activation. The peak amplitude distribution of AE hits has shown that hits with similar peak amplitude are generated for all strain rates.     

Deformation behaviour and new constitutive equation utilising the grain size of commercial TC6 titanium alloy

Abstract

Isothermal compression tests on a commercial TC6 titanium alloy have been conducted at deformation temperatures of about 800 – 1040°C, strain rates of 0.001 – 50 s^-1 and height reductions of 30 – 50%. The microstructural evolution is represented through the measured grain size of the prior α-phase. Meanwhile, a new constitutive equation, which includes the grain size, is established for high temperature deformation behaviour. The procedure required to formulate a constitutive equation from the experimental results is presented. The constitutive equation to model the behaviour of the TC6 titanium alloy during high temperature deformation is validated and its formulation is presented. The results show that the present equation is satisfactory for describing the behaviour of the TC6 titanium alloy during high temperature deformation. The maximum difference between the calculated and the experimental results is less than 15%.     

A constitutive model for high strain rate deformation in FCC metals based on irreversible thermodynamics

The present work extends a recent model for plastic deformation of polycrystalline metals based on irreversible thermodynamics. A general dislocation evolution equation is derived for a wide range of strain rates. It is found that there is a transitional strain rate (10³ s⁻¹) over which the phonon drag effects play a dominant role in dislocation generation resulting in a significant raise in the dislocation density and flow stress. The model reduces to the classical Kocks–Mecking model at low strain rates.     

Hot deformation behaviour of precipitation hardening stainless steel

Abstract

The behaviour of 17-4 precipitation hardening (PH) stainless steel was studied using the hot compression test at temperatures of 950–1150°C with strain rates of 0·001–10 s^?1. The stress–strain curves were plotted by considering the effect of friction. The work hardening rate versus stress curves were used to reveal whether or not dynamic recrystallisation (DRX) occurred. Using the constitutive equations, the activation energy of hot working for 17-4 PH stainless steel was determined as 337 kJ mol^?1. The effect of Zener–Hollomon parameter Z on the peak stress and strain was studied using the power law relation. The normalised critical stress and strain for initiation of DRX were found to be 0·89 and 0·47 respectively. Moreover, these behaviours were compared to other steels.     

A variational,finite‐deformation constitutive model for piezoelectric materials

We present a constitutive model for piezoelectric materials. The model is fully variational and supports finite kinematics. The postulated free energy depends on the deformation mapping and an electric vector potential, from which the strain and the electric displacement are derived, respectively. The divergence‐free condition of the electric vector potential is enforced by means of a penalty method, which leads to a positive definite tangent for the system of equations that represent the problem. The performance of the formulation is demonstrated by several examples. Published in 2010 by John Wiley & Sons, Ltd.     

Reinvestigation of dynamic materials model analysis of 99.94% purity aluminium

Abstract

This paper explains the drawbacks in the recent investigations carried out by Puchi et al. on the dynamic materials modelling concepts applied to analysis of hot rolling of commercial aluminium alloys.     

A micromechanical constitutive model for dynamic damage and fracture of ductile materials

This paper proposes a detailed theoretical analysis of the development of dynamic damage in plate impact experiments for the case of high-purity tantalum. Our micro-mechanical model of damage is based on physical mechanisms (void nucleation and growth). The model is aimed to be general enough to be applied to a variety of ductile materials subjected to high tensile pressure loading. In this respect, the work of Czarnota et al. (J Mech Phys Solids 56:1624–1650, 2008) has been extended by introducing the concept of nucleation law and by entering a nonlinear formulation of the elastic response based on the Mie-Grüneisen equation of state. This later aspect allows us to consider high impact velocities. All model parameters are directly assessed by experimental measurements to the exception of the nucleation law which is characterized by the way of an inverse identification method using three free-surface velocity profiles (at low, intermediate and high impact velocities). It is shown that the nucleation law can be consistently determined in the range of operating pressures. The nucleation law being identified, the development of internal damage happens to be a natural outcome of the modelling. The model is applied to predict damage development and free-surface velocity profiles for various test conditions. The variety and the quality of results support the physical basis (in particular micro-inertia effects) upon which the proposed model of dynamic damage is based.     

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.     

A model of the high-temperature deformation of metallic materials with ellipsoidal second-phase particles

A micromechanics model developed in the previous work which incorporated the effect of dynamic recovery by diffusion of atoms was applied to the interpretation of the high-temperature deformation of metallic materials with ellipsoidal second-phase particles. A theoretical discussion based on this model was made on the effect of several factors including shape, particle size, orientation and elastic modulus of second phase on the work-hardening behaviour of the materials at high temperature. A good correlation was found between the result of the calculations and those of the experiments obtained by the present authors or other investigators of several kinds of metallic materials with ellipsoidal second-phase particles. The dynamic recovery model used in this study can be applied to the understanding of high-temperature deformation behaviour or to the prediction of the possible recovery mechanism of the materials.     

Model of damage cumulation in metallic materials under static tension

The article deals with a new phenomenological model of damage cumulation in metallic materials subjected to static tension. The main parameter of the running state of the material, which is put in correspondence with the degree of loosening, is the Poisson ratio at the stage of loss of strength (the descending part of the stress-strain curve). The suggested model describes satisfactorily the results of specially arranged experiments.Translated from Problemy Prochnosti, No. 7, pp. 31–40, July, 1995.     

A new multiaxial fatigue damage model for various metallic materials under the combination of tension and torsion loadings

Based on the critical plane approach, a new damage parameter for multiaxial fatigue damage is presented. Both components of strain and stress are considered in this parameter. Thus, a new multiaxial fatigue damage model is given based on the critical plane approach. The capability of fatigue life prediction for the proposed fatigue damage model is checked against the experimental data of Hot-rolled 45 Steel, S460N Steel, 1045HR Steel, 30CrMnSiNi2A alloy steel, and GH4169 alloy at elevated temperature, and the predicted results are compared with results from common multiaxial fatigue model. It is demonstrated that the proposed criterion gives better satisfactory results for all the five checked materials.     

A model of damage accumulation in metallic materials in the complex stressed state

A phenomenological model of damage accumulation in metallic materials under static loading was proposed earlier by Lebedev et al. (Probl. Prochn., No. 7, pp. 31–40, 1995). According to this model, the dependence of the degree of damage to the material on strains has the formε _l ^p = [1 − 2μ(ε)]ε, where μ(ε) is the current value of the coefficient of shear strains. We generalize this model to the case of a complex stressed state by introducing an influence functionf(σ _ij ) which reflects the distinctive features of the evolution of structures depending on the type of the stressed state. Numerical results are in good agrement with experimental data, which proves that the theoretical assumptions are correct. Translated from Problemy Prochnosti, No. 3, pp. 55–63, May–June, 1997.     

A large deformation breakage model of granular materials including porosity and inelastic distortional deformation rate

A general constitutive model of crushable granular materials is developed within the context of large deformations. The time evolution equations for breakage, inelastic porous compaction and dilation, and distortional deformations are coupled by a yield surface and restrictions are imposed to ensure that these inelastic processes are dissipative. Some of the most salient mechanisms of such materials are described, including: (1) stiffness dependent on the breakage (a variable index of grading), porosity, and pressure; (2) critical comminution pressure and isotropic hardening, also dependent on the breakage and porosity; (3) jamming transition between solid and gaseous states; (4) a dilation law that embodies competition between porous compaction (due to the rate of breakage) and bulking (porous dilation at positive pressure due to the rate of inelastic distortional deformation); and finally, (5) the non-unique critical state relation between stress and porosity, in terms of the loading history and grading changes.     

Tensile and work hardening properties of low carbon dual phase strip steels at high strain rates

Abstract

As a result of their unique combination of strength and ductility dual phase steels play an important role in reducing weight in automobile components and improving crashworthiness. The purpose of this paper is to quantify the crash performance of dual phase steels, as defined by the influence of low and high strain deformation rates (0·001 s^-1 and 100 s^-1 respectively), on the tensile and work hardening properties of a range of commercial dual phase products. The objective is to establish whether dual phase steels maintain their desirable mechanical property characteristics of low yield strength, high tensile strength and high work hardening rates during plastic deformation under the application of a high strain rate loading. The results confirmed that the yield/proof strength and tensile strength increased with increasing volume fraction of second phase constituents and increasing strain rate. In particular, a dual phase steel with a microstructure consisting of a significant volume fraction (>10–15%) of additional second phase material (bainite) is shown to display superior energy absorption properties. However, this is accompanied by poor ductility and work hardening characteristics.