Thermo-viscoplastic constitutive relation for aluminium alloys, modeling of negative strain rate sensitivity and viscous drag effects

In this paper are presented two extensions of the Rusinek–Klepaczko constitutive relation [Rusinek A, Klepaczko JR. Shear testing of sheet steel at wide range of strain rates and a constitutive relation with strain-rate and temperature dependence of the flow stress. Int J Plasticity 2001;17:87–115] to define the behaviour of aluminium alloys at wide ranges of strain rate and temperature. The formulations reported extend the validity of the Rusinek–Klepaczko model for the definition of particular aspects of the behaviour of aluminium alloys, namely the negative strain rate sensitivity and the viscous drag. Such formulations are applied to describe the thermo-viscoplastic behaviour of two commercial aluminium alloys (AA 5083-H116 and AA 7075) using experimental data available in the literature [Clausen AH, Børvik T, Hopperstad OS, Benallal A. Flow and fracture characteristics of aluminium alloy AA5083-H116 as function of strain rate, temperature and triaxiality. Mater Sci Eng A 2004;364:260–72; El-Magd E, Abouridouane M. Characterization, modelling and simulation of deformation and fracture behaviour of the light-weight wrought alloys under high strain rate loading. Int J Impact Eng 2006;32:741–58]. Their analytical results are compared with those obtained from the phenomenological constitutive relations reported in Clausen et al. (2004) and El-Magd and Abouridouane (2006). The best agreement with experiments is achieved by the predictions provided by the extended Rusinek–Klepaczko models. Moreover, the formulations presented may be implemented into FE code using for example the algorithm reported in [Zaera R, Fernández-Sáez J. An implicit consistent algorithm for the integration of thermoviscoplastic constitutive equations in adiabatic conditions and finite deformations. Int J Solids Struct 2006;43:1594–612].     

Finite element simulation of fracture behaviour for aged duplex stainless steels

In this paper, the local approach model developed by Gurson–Tvergaard has been applied to simulate both the crack initiation and the crack growth of aged duplex stainless steel. The parameters of the Gurson–Tvergaard model have been obtained, from axisymmetric notched specimen testing, as a function of the ageing time at 400°C, the ferrite content of the steel and the stress triaxiality. After that, to simulate the fracture of CT specimens, finite element (FE) calculations have been effected in order to obtain the stress triaxiality value at each point on the process zone ahead of the crack tip of these specimens. The adequate damage parameters concerning triaxiality are determined from the ones obtained at the notched specimens, in order to be used in FE simulations of fracture behaviour. With them, the corresponding J−Δa curves have been simulated as representative of both the crack initiation and crack propagation stages, and compared with experimental results in order to validate the methodology proposed.     

A numerical study of ductile void growth under dynamic loading conditions

A numerical study of void growth at differing global strain rates in the range 149 s^–1–2240 s^–1 and at start temperatures between 173 K and 573 K has been carried out for a material containing a three-dimensional periodic array of equally spaced, initially spherical voids. To take account of the effect of strain rate and temperature on the flow stress under dynamic adiabatic conditions, the well-established Zerilli-Armstrong constitutive relations for pure copper and iron have been employed. An instability criterion based on the maximum mean tensile stress has been used to identify the point at which unstable void growth occurs. For both materials, the strain at instability has been found to be dependent on stress triaxiality and start temperature but only weakly affected by strain-rate     

Experimental investigation of fracture under controlled stress triaxiality using shear-compression disk specimen

Experimental investigation of the effect of stress triaxiality on fracture strain has been performed using the shear-compression disk (SCD) specimen. A series of experiments was carried out under quasi-static loading conditions at triaxiality levels in the range of \(-\,0.7\) to \(+\,0.05\). The experiments were designed to generate relatively uniform strain and triaxiality in the sheared zone of the specimen, and a constant level of triaxiality along the entire loading path. The results obtained for SAE 1045 steel are compared to previous studies on the same material which revealed considerable differences. Discussion on possible contributing factors to the differences, and the potential of the SCD specimen for fracture investigations are discussed.     

Thermomechanical treatment of 2014 aluminium alloy

Abstract

The effect of thermomechanical treatment on the flow stress, fracture strain, structure, and precipitation behaviour of commercial grade 2014 aluminium alloy has been investigated. Specimens in the supersaturated and aged conditions were plastically deformed in torsion tests in the temperature range 293–493 k and strain rate range 2·8 ×10^?3?2·5 s^?1. It is stated that the starting condition of the alloy acts dominantly on the flow stress, fracture strain, and thermally activated processes, which take place during aging. An increase in temperature results mainly in a reduction of flow stress in the aged alloy and an increase in flow stress in the supersaturated alloy. The supersaturated alloy exhibits negative strain rate sensitivity over the entire range of applied temperature while for the aged alloy it is exhibited only in the temperature range 293–393 K. The effect of temperature and strain rate on the fracture strain of the supersaturated alloy is negligible, but the fracture strain of the aged alloy increases with temperature and decreases with strain rate. In the supersaturated alloy, the process of strain aging is dominant during deformation at room temperature and at higher temperatures precipitation aging and recovery are dominant. In the aged alloy, strain aging is dominant in the temperature range 293–443 K and recovery is dominant only at the highest test temperature (493 K).

MST/616     

Studies on the development of aluminium alloy–mild steel reinforced composite

With a view to developing a new metal–metal cast composite material as a possible substitute for ferrous materials in wear resistant applications, Al alloy (LM11) is reinforced with mild steel (ms) wires and it is heat treated to get ‘reaction interface’ (RI). Microhardness, tensile properties and wear characteristics of the matrix, as-cast and heat treated composites have been determined. While microhardness of the composite showed variation from 150 to 45 VHN across the interface in the as-cast composite, annealed (500–525°C) composite showed a microhardness of 350–420 VHN at the interface indicating the effectiveness of the heat treatment. It is seen that the % improvement in wear resistance increased with increase in number of wires when embedded in the aluminium alloy matrix. Further imrpovement of about 30% was observed when heat treated at 500°C for 15 h. These results have been discussed in terms of wetting between ms wires and the matrix, particularly the increase of hardness and tensile strength to the formation of ‘reaction interface’ due to annealing. The width of the interface increased with annealing time and temperature and the kinetics of reaction followed logarithmic and parabolic growth rate. The activation energy for the formation of intermetallics constituting the reaction interface is found to be 20.7 KJ mol⁻¹. From the measured hardness and ultimate tensile strength of the constituents and composites an empirical relation was deduced.     

Generalized fracture mechanics

The application of generalized fracture mechanics to ductile materials is considered. The deformations leading to crack propagation in SEN specimens of a copper-beryllium alloy in two conditions were established experimentally and can be described in terms of the generalized theory. In particular, it was possible to define and measure a surface work for fracture propagation in specimens subject to general yielding. The values of surface work obtained were 7.5×10⁸ mJ m^–2 for the alloy in a low yield stress (235 MPa) condition and 1.2×10⁸ mJ m^–2 for the high yield-stress (725 MPa) condition.On secondment from RARDE (Ministry of Defence) Fort Halstead, Sevenoakes, Kent.     

Production of cast aluminium-graphite particle composites using a pellet method

Copper- and nickel-coated graphite particles can be successfully introduced into aluminium-base alloy melts as pellets to produce cast aluminium-graphite particle composites. The pellets were made by pressing mixtures of nickel- or copper-coated graphite particles and aluminium powders together at pressures varying between 2 and 20 kg mm^–2. These pellets were dispersed in aluminium alloy melts by plunging and holding them in the melts using a refractory coated mild steel cone, until the pellets disintegrated and the powders were dispersed. The optimum pressure for the preparation of pellets was 2 to 5 kg mm^–2 and the optimum size and percentage of aluminium powder were 400 to 1000m and 35 wt% respectively. Under optimum conditions the recovery of the graphite particles in the castings was as high as 96%, these particles being pushed into the last freezing interdendritic regions. The tensile strength and the hardness of the graphite aluminium alloys made using the pellet method are comparable to those of similar composites made using gas injection or the vortex method. The pellet method however has the advantage of greater reproducibility and flexibility. Dispersion of graphite particles in the matrix of cast aluminium alloys using the pellet method increases their resistance to wear.Formerly with Indian Institute of Science, Bangalore, India.     

Effect of residual stress on the strength of alumina-steel joint with Al-Si interlayer

The effect of residual stress on the strength of an alumina-steel joint with the Al-Si interlayer was studied. Alumina rods, 32 mm in diameter and 9 mm in length and steel pipes were diffusion bonded at 873 K and at a contact pressure of about 5 M Pa for 30 min in a vacuum of 24×10^–2Pa. The interlayer of aluminium sheet clad with Al-10% Si alloy on both sides was used. The tensile strength of the joints is influenced by the thickness of the interlayer or the intermetallic compound formed between the interlayer and the steel. The strength increases with increasing interlayer thickness and with decreasing intermetallic compound thickness. It is found that the residual stress measured by Sachs method is much lower than that by the elastic calculation. The stress decreases with increasing interlayer thickness. Increase in thickness of the aluminium core of the interlayer is effective in improving the joint strength. This improvement can be explained by considering the stress of the joint.     

High-strain-rate superplastic deformation behavior of a powder metallurgy-processed 2124 Al alloy

High-strain-rate superplastic behavior of a powder-metallurgy processed 2124 alloy prepared through extrusion at a high ratio of 70 : 1 was investigated. A maximum tensile elongation of 700% was obtained at 823 K and at a strain rate of 10^–2 s^–1. Deformation behavior of this alloy was similar to those reported for other many HSR superplastic materials. Incorporation of threshold stress into the constitutive equation reveals that the true stress exponent is 2 and true activation energy for plastic flow is comparable to that for lattice diffusion in pure aluminum. Comparison of the present alloy with the 2124 Al composite indicates that the composite is weaker than the unreinforced alloy in the temperature range where grain boundary sliding is rate-controlled.     

Fracture characteristics of a burst tested maraging steel rocket motor case

A 0.3 m diameter, 2 m long and 0.0015 m thick, 18 nickel 1800 MNm^–2 grade maraging steel motor case was designed, fabricated and burst tested to gain experience for using the steel as booster case material in satellite launch vehicles. The bursting occurred at 15.2 MPa for which the effective hoop stress worked out to be 1754 MNm^–2 almost equal to the ultimate tensile strength (1764 MNm^–2) of the material in the solution treated and aged condition. The failure analysis revealed that the material failed due to normal tensile overload fracture. The burst test data was used to arrive at fracture mechanics parameters like crack size, gross section area stress and the stress for leak before bursting.     

Fracture of austenitic steel subject to a wide range of stress triaxiality ratios and crack deformation modes

The stress triaxiality ratio (hydrostatic pressure divided by von Mises equivalent stress) strongly affects the fracture behaviour of materials. Various fracture criteria take this effect into consideration in their effort to predict failure. The dependency of the fracture locus on the stress triaxiality ratio has to be investigated in order to evaluate these criteria and improve the understanding of ductile fracture.This was done by comparing the experimental results of austenitic steel specimens with a strong variation in their stress triaxiality ratios. The specimens had cracks with varying depths and crack tip deformation modes; tension, in-plane shear, and out-of-plane shear. The crack growth in fracture mechanics specimens was compared with the failure of standard testing specimens for tension, upsetting and torsion. By associating the experimental results with finite element simulations it was possible to compare the critical plastic equivalent strain and stress triaxiality ratio values at fracture. In the investigated triaxiality regime an exponential dependency of the fracture locus on the stress triaxiality ratio was found.     

Microstructure and internal friction of spray deposited Al-3.3Fe-10.7Si alloy

Al-3.3Fe-10.7Si alloy has been experimentally made with spray deposition technology. The internal friction of the alloy which was directly associated with the microstructures under spray deposited, extruted and heat treated conditions has been investigated using a low frequency inverted torsion pendulum over the temperature region of 10–300 °C. An internal friction peak was observed in the temperature range 50–250 °C in the present alloy. The Q^-1 peak decreased after extruted and in subsequent to the earliness of isothermal annealing, which was found to be directly attributed to the precipitation of FeAl₂ and Al– Fe– Si intermetallics from the supersaturated aluminium alloy matrix. We suggest that the internal friction peak in the alloy originates from grain boundary relaxation, but the grain boundary relaxation can also be affected by FeAl₂ and Al– Fe– Si intermetallics at the grain boundaries, which will impede grain boundary sliding.     

Experimental and numerical investigation on ductile-brittle fracture transition in a magnesium alloy

Tensile test on smooth and circumferentially notched specimens, systematic observation of fracture surfaces and large deformation finite element analysis were conducted to understand the deformation and failure behavior of a magnesium alloy (AM60). The plastic deformation is considered to be dominated by twining mediated slip. The tensile properties were not sensitive to the strain rates applied (3.3 × 10⁻⁴∼0.1). Corresponding to the same loading level, higher stress triaxiality but lower plastic strain was observed in the specimens with a smaller notch profile radius. Deformation and failure of the magnesium alloy were sensitive to the constraint level and ductile-brittle fracture transition occurred with decreasing the notch profile radius.     

Investigation of fracture mechanism of 6063 aluminum alloy under different stress states

Fracture mechanisms in a 6063 aluminum alloy were investigated and analyzed carefully by in-situ tensile tests in SEM with a vacuum chamber. Specimens used were designed to produce different stress states. Studies indicated that with stress triaxiality (σ _m/σ _e) decreasing, the fracture modes changed from normal fracture to shear fracture and the fracture surfaces changed from the dimples and intragranular dominated fracture mode to the shear dominated fracture mode. The grain boundaries of the 6063 aluminum alloy were the weakest positions. In the case of high stress triaxiality, the grain boundary cracks were produced by normal stress or by the incompatibility of deformation between neighboring grains, and the normal stress dominated the crack propagation. In the case of low stress triaxiality, the boundary cracks were produced by the relative slipping of grains against neighboring grains, and the shear stress dominated the crack propagation. The final fracture of the specimens occurred by connections of cracks through transgranular cracking of the ligaments among these cracks.     

Effect of cutting speed and tool rake angle on residual stress distribution in machining 2024-T351 aluminium alloy — unlubricated conditions

The residual stress distribution in the machining of 2024-T351 aluminium alloy was measured using an electrolytic etching technique. Ring-shape specimens were machined under unlubricated orthogonal conditions with high-speed steel tools having rake angles of 10, 15, 20 and 25° at cutting speeds ranging between 0.5 and 1.25 m sec^–1. The results of the investigation show that the residual stresses are compressive at the machined surface and decrease with depth beneath the machined surface. The maximum (near-surface) residual stress and the depth of the severely stressed region increase with an increase in the cutting speed. There seems to be little change in the residual stress distribution due to a change in the rake angle. The results are interpreted in terms of the variations in the amount of surface-region deformation produced by changes in cutting conditions.     

Axi-symmetric compression of solid cylinders

Cylinders of EN 24 steel and commercial aluminium were compressed at 0.2 and 10.0 s⁻¹ (rapid loading conditions). The temperature rise due to plastic deformation increased with strain rate and was significantly more in steel than in aluminium. The shape of the observed true stress-true strain curves was similar to the temperature rise-true strain plots. In steel, beyond a certain strain, the flow stress decreased with increasing strain, but in aluminium, a direct relation between the observed true stress and the true strain existed over the entire deformation range. Under rapid loading conditions the ring compression test was more reliable than the Cook and Larke method. In both materials, in specimens of constant diameter up to a true strain of 30%–40%, the compressive yield stress, σ_o, was proportional to H^1/8, where H is the instantaneous height of the specimen. Beyond this strain level, σ_o increased with the diameter-to-height ratio (as seen during slow loading). The various factors that can influence the shape of the observed true stress-true strain curves have been considered. Semi-empirical equations have been developed which ensured that the friction-corrected data covering four to five decades of strain rate superimposed fairly well, following suitable temperature or temperature and strain-rate corrections.     

Nucleation and propagation of fatigue cracks in Al-304 stainless steel laminate composite

A study has been made of fatigue crack nucleation and propagation in Al-stainless steel (30 vol%) laminate composites. A Paris type power relationship between the crack growth rate, da/dN, and the alternating stress intensity, K, was obtained over the crack growth rates ranging from 10^–7 to 10^–4 mm/cycle, with an exponentm of 2.7. The cracks nucleated first in Al strips and then in stainless steel strips accompanied by some interface decohesion. The fatigue crack propagated in two stages. In the first stage, where the Al-steel interface was largely intact, the crack propagated in a plane strain mode (flat fracture surface with striations, each striation consisting of a cluster of interstriations). In the second stage, where there occurred extensive Al-steel interface delamination and the concomitant loss of mutual constraint, the crack propagated in the plane stress mode (slant fracture with voids). The crack growth was faster in Al than that in steel since the apparent striation spacing was larger in the former than in the latter. No one to one correspondence existed between the apparent striation spacing and the macroscopic crack growth rate.Thus, although, microscopically, the crack front was not planar; macroscopically, it could be regarded as planar, and a Paris type power relationship did characterize the macroscopic fatigue crack growth in this laminate system over the applied stress amplitude studied. Comparing the fatigue crack growth rates among Al-steel laminate, commercial or pure aluminium and 304 stainless steel, the Al-steel laminate has the lowest crack growth rate. This plus the weight and cost saving benefits make Al-steel laminate quite attractive.     

Fatigue crack propagation in polymeric materials

In order to gain a better understanding of matrix-controlled fatigue failure processes in non-metallic materials a series of fatigue tests were performed on several different polymer materials representing different classes of mechanical response. Fatigue crack propagation rates between 5×10^–6 in. cycle^–1 (127 nm cycle^–1) and 4×10^–4 in. cycle^–1 (10 300 nm cycle^–1) were measured in nylon, polycarbonate, ABS resin, low-density polyethylene and polymethyl methacrylate. A strong correlation was found between the fatigue crack propagation rate and the stress intensity factor range prevailing at the advancing crack tip. Whereas metals exhibit comparable fatigue growth rates for a given stress intensity range when normalised with respect to their static elastic modulus, the polymer materials exhibited a 1300-fold difference in crack growth rate for a given normalised stress intensity range. This observation dramatically illustrates the importance of understanding molecular motion and energy dissipation processes in polymer materials as related to their chemistry and architecture. The relative behaviour of the different polymer materials could be generally correlated with their reported damping characteristics.     

Influence of the microstructure of aluminium alloys on their residual impact properties after a fatigue loading program

Consecutive loadings of fatigue and impact have been carried out on aluminium alloys. The aim of this study is to quantify the influence of the microstructure on the residual impact behavior after a prior fatigue loading. Two alloys with different chemical compositions and hardening modes have been investigated: 2017A-T3 used in the aircraft industry and 5454-O used in automotive applications.The fatigue pre-loadings were carried out under fully reversed tensile-compression with several pairs (stress level, number of cycles) in the high cycle fatigue zone (10⁵– 10⁶cycles). The residual impact behavior was determined under tensile loading, in the range of medium strain rates (about ). To assess the prior fatigue damage and to follow its evolution during the impact loading, observation of the specimens (surface and fracture surfaces) were made.From this study, two conclusions have been highlighted: (1) there is no direct correlation between a given prior loading and residual behavior, whatever the material; (2) the material aspect is fundamental. At the mechanical (macroscopic) scale, the Al–Mg alloy (5454-O) remains insensitive to the prior fatigue loading whereas the Al–Cu alloy (2017A-T3) undergoes a large modification in its residual performance. At a lower scale, the pre-damage signature appears for the insensitive as well as for the sensitive material. The prior damage and its contribution to the process fracture appear to be strongly linked with the material’s microstructure.