A strain-energy-density-based lifetime prediction model for notched specimens: Polycarbonate under thermal fatigue

Polycarbonate is more and more extensively used in engineering because of its good mechanical properties. Pieces of polycarbonate are used in environments with variable temperature, especially in electronic devices. Thermal stresses could become important and, for this reason, the effects of thermal stresses must be taken into account in designing these pieces. We propose a method for the prediction of the life of notched specimens based on the density of dissipated strain energy. The laws of behavior of polycarbonate at various temperatures are determined, and the fatigue tests performed on smooth specimens give the laws of thermal fatigue of the material. The fatigue tests on notched specimens and finite-element-method computations enable us to establish the relationship between the stress concentration factor, the density of strain energy dissipated at the notch roots, and the density of nominal strain energy. A life-prediction model is proposed and discussed. Laboratory of Mechanical Reliability, Metz University, Metz, France. Published in Problemy Prochnosti, No. 6, pp. 32–42, November–December, 1998.     

Viscoplastic behaviour of metals deformed at high-temperature, application to tension–compression cycles

A mechanical modelling is proposed in order to describe viscoplastic behaviour without hardening of a nickel-base super alloy loaded at high temperature (900 °C) with strain rates varying within a wide range (from 10⁻¹ to 10⁻⁴ s⁻¹). A mathematical law is associated to the viscoplastic model; the parameters of the law are identified from monotonic biaxial tests of membranes loaded by pressure of inert gas (disk pressure testing under helium). The viscoplastic law provides calculated stresses with accuracy better than 1% at the highest strain rates and 4% at the lowest strain rates; the identified yield stress is a logarithmical function of strain rate as for other metallic alloys studied in the bibliography. The parameters identified from biaxial tensile tests of disks have been successfully used to calculate the stresses during stabilized tension–compression loops of cylindrical specimens. The proposed experimental method and behaviour model are interesting because the disk biaxial testing is much more easily performed at high temperature than the tension–compression testing of cylindrical specimens.     

Prediction of hot deformation behavior of Al–5.9%Cu–0.5%Mg alloys with trace additions of Sn

High temperature deformation behavior of Al–5.9wt%Cu–0.5wt%Mg alloys containing trace amounts (from 0 to 0.1 wt%) of Sn was studied by hot compression tests conducted at various temperatures and strain rates. The peak flow stress of the alloys increased with increase in strain rate and decrease in deformation temperature. The peak stress could be correlated with temperature and strain rate by a suitable hyperbolic-sine constitutive equation. The activation energy for hot deformation of the alloy without Sn content was observed to be 183.4 kJ mol⁻¹ which increased to 225.5 kJ mol⁻¹ due to 0.08 wt% of Sn addition. The Zener-Hollomon parameter (Z) was determined at various deforming conditions. The tendency of dynamic recrystallization increased with low Z values, corresponding to low strain rate and high temperature. The peak flow stresses at various processing conditions have been predicted by the constitutive modeling and correlated with the experimental results with fairly good accuracy. It was possible to predict 80, 75, 100, 100, 90, and 85% of the peak stress values within an error less than ±13%, for the investigated alloys. With addition of Sn content >0.04 wt%, peak flow stress increased significantly for all strain rate and temperature combinations. Scanning electron microscope revealed two types of second phases at the grain boundary of the undeformed alloy matrix, one being an Al–Cu–Si–Fe–Mn phase while the other identified as CuAl₂. The high strength and flow stress value of the alloy with 0.06 wt% of Sn content, may be attributed to the variation in amount, composition, and morphology of the Al–Cu–Si–Fe–Mn phase, as well as to the lower value of activation energy for precipitation reaction, as revealed from differential scanning calorimetric studies.     

Effect of strain rate and environment on the mechanical properties of the Ni–19Si–3Nb–0.15B–0.1C intermetallic alloy at high temperatures

The effect of strain rate and environment on the mechanical behavior at different temperatures of the Ni–19Si–3Nb–0.15B–0.1C alloy is investigated by atmosphere-controlled tensile testing under various conditions at different strain rates and different temperatures). The results reveal that the Ni–19Si–3Nb–0.15B–0.1C alloy exhibits ductile mechanical behavior (UTS ∼ 1250 MPa, ε ~ 14%) at temperatures below 873 K under different atmosphere conditions. However, the alloy without boron and carbon addition shows ductile mechanical behavior only when the sample is tested in vacuum. This indicates that the microalloying of boron and carbon does overcome the environmental embrittlement from water vapor at test temperatures below 873 K for the Ni–19Si–3Nb base alloy. However, the boron and carbon doped alloy still suffers from embrittlement associated with oxygen at a medium high temperature (i.e. 973 K). In parallel, both of the ultimate tensile strength and elongation exhibit quite insensitive response with respect to the loading strain rate when tests are held at temperatures below 873 K. However, the ultimate tensile strength exhibits high dependence on the strain rate in air at temperatures above 873 K, decreasing the ultimate tensile strength with decreasing strain rate.     

On the plane problem approximation in the theory of macroisotropic composite material

A plane problem approximation is studied with mean, over the volume of phases, stresses in a two-phase macroisotropic composite material. Numerical results for WC-Co hard metals with a boundary type microstructure are analyzed. The microstresses as determined within the plane strain approach can be higher than the true stresses in the case of simple shearing strain but lower than the true stresses in the case of a uniaxial stressed state; the residual thermal stresses are smaller than the true residual stresses. The stresses estimated by the two-and three-dimensional approaches tend to equalize as the cobalt binder amount is raised. __________ Translated from Problemy Prochnosti, No. 1, pp. 13–21, January–February, 2007.     

Processing maps for Fe–24Ni–11Cr–3Ti–1Mo superalloy

Hot deformation characteristics of a Fe-base superalloy were studied at various temperatures from 1000–1200°C under strain rates from 0·001–1 s^− 1 using hot compression tests. Processing maps for hot working are developed on the basis of the variations of efficiency of power dissipation with temperature and strain rate and interpreted by a dynamic materials model. Hot deformation equation was given to characterize the dependence of peak stress on deformation temperature and strain rate. Hot deformation apparent activation energy of the Fe–24Ni–11Cr–1Mo–3Ti superalloy was determined to be about 499 kJ/mol. The processing maps obtained in a strain range of 0·1–0·7 were essentially similar, indicating that strain has no significant influence on it. The processing maps exhibited a clear domain with a maximum of about 40–48% at about 1150°C and 0·001 s^− 1.     

Preliminary thermomechanical loading (warm prestressing) as a promising method for increasing the radiation resistance of the vessels of water-moderated water-cooled power reactors operating under high pressure

We study the influence of various modes of preliminary thermomechanical loading (warm prestressing) on the brittle-fracture resistance of heat-resistant pressure-vessel reactor steels with different levels of embrittlement induced by thermal treatment. The tests were performed on specimens 25, 50, and 150 mm in thickness with short and long cracks of various shapes in the temperature range 293–623 K, corresponding to the service temperatures of these types of steel. We analyzed the contributions of different mechanisms (such as residual stresses, strain hardening, and crack-tip blunting) to an increase in the brittle-fracture resistance of the investigated types of steel subjected to warm prestressing, the stability of the positive effect of warm prestressing for various times of holding of these metals under different working loads and at different temperatures, and the influence of the sizes of specimens on the optimal modes of warm prestressing and the characteristics of brittle-fracture resistance of steels after thermomechanical treatment. We propose an approach to the prediction of the influence of the modes of thermomechanical treatment on the behavior of the brittle-fracture resistance of cracked steels. Translated from Problemy Prochnosti, No. 2, pp. 38 – 55, March – April, 1998.     

A method for low-cycle fatigue life assessment of metallic materials under multiaxial loading

A new method of fatigue life assessment under multiaxial low-cycle regular and irregular loading is proposed, which is based on the modified Pisarenko-Lebedev criterion, the linear damage accumulation hypothesis, and the nonlinear Manson approach. The results of low-cycle fatigue tests of titanium alloy VT9 under irregular proportional and non-proportional biaxial loading are given. The tests were carried out at three Mises strain levels (0.6, 0.8, and 1.0%) with various combinations of proportional and non-proportional strain paths. All the tests were carried out at room temperature. The proposed method turned out to be effective and to allow for such factors as strain state type, strain path type and loading irregularity. __________ Translated from Problemy Prochnosti, No. 1, pp. 56–59, January–February, 2008.     

Effect of temperature on the viscoelastic and viscoplastic behavior of polypropylene

Observations are reported on isotactic polypropylene in tensile tests with various cross-head speeds and relaxation tests in a wide interval of temperatures ranging from room temperature to 120°C. A constitutive model is derived for the viscoelastic and viscoplastic responses of a semicrystalline polymer at arbitrary deformations with small strains. The stress–strain relations involve 6 adjustable parameters that are found by fitting the experimental data. The presence of a critical temperature is demonstrated at which some parameters of the model reach their maxima. This temperature is associated with the α-relaxation temperature of polypropylene.     

Material characterization of SS 316 in low-cycle fatigue loading

This study deals with simulation of low-cycle fatigue (LCF), followed by evaluation of fatigue parameters, which would be suitable for estimating fatigue lives under uniaxial loading. The cyclic elastic–plastic stress–strain responses were analyzed using the incremental plasticity procedures. Finite-element (FE) simulation in elastic–plastic regime was carried out in FE package ABAQUS. Emphasis has been laid on calibration of SS 316 stainless steel for LCF behavior. For experimental verifications, a series of low-cycle fatigue tests were conducted using smooth, cylindrical specimens under strain-controlled, fully reversed condition in INSTRON UTM (Universal Testing Machine) with 8,800 controller at room temperature. The comparisons between numerical simulations and experimental observations reveal the matching to be satisfactory in engineering sense. Based on the cyclic elastic–plastic stress–strain response, both from experiments and simulation, loop areas, computed for various strain amplitude, have been identified as fatigue damage parameter. Fatigue strain life curves are generated for fatigue life prediction using Coffin–Manson relation, Smith–Watson–Topper model, and plastic energy dissipated per cycle (loop area). Life prediction for LCF has been found out to be almost identical for all these three criteria and correlations between predicted and experimental results are shown. It is concluded that the improvement of fatigue life prediction depends not only on the fatigue damage models, but also on the accurate evaluations of the cyclic elastic–plastic stress/strain responses.     

Experiments and simulations of uniaxial ratchetting deformation of Sn–3Ag–0.5Cu and Sn–37Pb solder alloys

This paper discusses uniaxial ratchetting deformation of lead-free solder alloy Sn–3Ag–0.5Cu and lead-containing solder alloy Sn–37Pb, which were subjected to tension–compression loading with several stress amplitudes and stress ratios, minimum stress over maximum stress. First the uniaxial ratchetting tests were conducted with three maximum stresses and four stress ratios. All tests were conducted using cylindrical bulk specimens of the solder alloys at 313 K. The test results show that there are differences in the ratchetting deformation behavior of the two solder alloys; the larger ratchetting strain occurs in the lead-containing solder alloy than in the lead-free solder alloy. The ratchetting deformation was simulated by the dislocation based constitutive model proposed by Estrin et al. (J Eng Mater Technol 118:441, 1996). The evolution equation of the back stress employed in the constitutive model was modified considering a dynamic recovery term. The effect of the modification of the back stress evolution is discussed by comparing the simulations with the corresponding experimental results. The simulations suggest that the recovery term in the kinematic hardening rule plays an important role in fitting the simulation to the experimental results of the ratchetting deformation of the solder alloys.     

Nature of splashes of microinhomogeneous strain in steel with nonmetallic inclusions

We study the distribution of microinhomogeneous strain in steel near nonmetallic inclusions of various types, which are not susceptible to the formation of hollows. We establish the features of the influence of temperature, plasticity of inclusions, and intersurface stresses on the distribution of microinhomogeneous strain. We study the nature of splashes of microstrains caused by fracture of inclusions and development of sliding along inclusion-matrix interfaces. Ukrainian Metallurgical Academy, Dnepropetrovsk. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 2, pp. 53–59, March–April, 1999.     

Deformation behavior of spray-formed hypereutectic Al–Si alloys

The deformation behavior of spray-formed hypereutectic aluminum–silicon alloys—AlSix (x = 18, 25, and 35 wt%)—has been studied by means of compression test at various temperatures and strain rates. The flow stress of the spray-formed Al–Si alloys increases with decreasing compression temperature and increasing strain rate. Higher silicon content in the alloys also leads to higher flow stress during deformation. The flow curves determined from the compression tests exhibit that the deformation of the materials is controlled by two competing mechanisms: strain hardening, and flow softening. Particle damage during the deformation may have an influence on the flow curves of the alloys with large silicon particles. Based on the flow curves obtained from the compression tests and knowledge of aluminum extrusion, the spray-formed hypereutectic Al–Si alloy billets have been hot extruded into wires with a high area reduction ratio around 189. Since primary silicon particles were greatly refined and uniformly distributed in the spray-formed materials, the heavy deformations of the spray-formed Al–Si alloys containing high amount of silicon were successfully performed.     

Viscoelasticity, viscoplasticity, and creep failure of polypropylene/clay nanocomposites

Observations are reported on polypropylene/clay nanocomposites in tensile tests with various strain rates, relaxation tests at various strains, and creep tests with various stresses at room temperature. New constitutive equations are derived in viscoelasticity and viscoplasticity of nanocomposites. Adjustable parameters are found by fitting the experimental data. The stress–strain relations are applied to the analysis of creep rupture. It is demonstrated that reinforcement of polypropylene with 1 wt.% of nanoclay induces an increase in time to failure by an order of magnitude.     

A simple orthotropic finite elasto–plasticity model based on generalized stress–strain measures

 In this paper we present a formulation of orthotropic elasto-plasticity at finite strains based on generalized stress–strain measures, which reduces for one special case to the so-called Green–Naghdi theory. The main goal is the representation of the governing constitutive equations within the invariant theory. Introducing additional argument tensors, the so-called structural tensors, the anisotropic constitutive equations, especially the free energy function, the yield criterion, the stress-response and the flow rule, are represented by scalar-valued and tensor-valued isotropic tensor functions. The proposed model is formulated in terms of generalized stress–strain measures in order to maintain the simple additive structure of the infinitesimal elasto-plasticity theory. The tensor generators for the stresses and moduli are derived in detail and some representative numerical examples are discussed. Received: 2 April 2002 / Accepted: 11 September 2002     

Analysis of pulse current-induced tensile stress relaxation

A procedure is offered and results of experimental evaluation of high-density pulse current effects on electrical resistance and relaxation of tensile elastic stresses are presented for a number of metallic materials. Based on analysis of experimental data, plastic strain rates are shown to be influenced by tensile stresses, current density, and temperature. __________ Translated from Problemy Prochnosti, No. 1, pp. 116–127, January–February, 2006.     

Superplastic power-law creep of Sn–40%Pb–2.5%Sb peritectic alloy

The power law-creep behavior of superplastic Sn–40Pb–2.5Sb alloys with different grain sizes has been investigated at room temperature. Stress exponent values for these alloys have been determined by indentation creep, conventional creep and uniaxial tension tests in order to evaluate the correspondence of indentation creep results with conventional tests. In all cases, the indentation results were in good agreement with each other and with those of the tensile and conventional creep tests. The average stress exponent values of about 2.6 and 3.0 corresponding to the strain rate sensitivity (SRS) indices of 0.33–0.39, depending on the grain size of the materials, indicate that the grain boundary sliding is the possible mechanism during creep deformation of Sn–Pb–Sb alloys. Within limits, the indentation tests are thus considered useful to acquire information on the creep behavior of small specimens of these soft tin–lead–antimony alloys at room temperature. It is also demonstrated that the indentation creep test provides a convenient method to measure SRS and thereby to assess the ability of a material to undergo superplastic deformation.     

Determination of large deformation and fracture behaviour of starch gels from conventional and wire cutting experiments

Large deformation and fracture properties of two types of starch gels were investigated through uniaxial compression, single edge-notched bend (SENB) and wire cutting experiments. Tests were performed at various loading rates and for various starch/powder concentrations (%w/w). It was found that starch gels exhibit rate independent stress–strain behaviour but show rate-dependent fracture behaviour, i.e. stress–strain curves at three loading rates are similar but fracture stress and fracture strain increase with increasing strain rate. This is rather unusual and interesting behaviour. SENB and wire cutting experiments also revealed rate-dependent fracture behaviour and that the true fracture toughness (G _c) values increase with loading/cutting speeds and starch powder concentration. In addition, the G _c values from wire cutting and SENB tests were in reasonable agreement. The wire cutting process was also studied numerically using finite element techniques. A non-linear elastic constitutive relationship based on Ogden was used to model the starch gels and a frictionless condition was assumed at the wire–starch gel contact interface. A fracture criterion based on maximum principal strain was assumed for the prediction of the steady state cutting force.     

Analysis of the creep and long-term strength of VT6 titanium alloy with preliminarily injected hydrogen

We describe the results of experimental and theoretical investigation of the influence of the concentration of preliminarily injected hydrogen on the creep and long-term strength of VT6 titanium alloy under the action of tensile stresses equal to 47–217 MPa. The tests carried out at a temperature of 600°C show that hydrogen (up to 0.3 wt.%) strongly decreases the steady-state creep rate of this alloy, increases the time to fracture, and lowers (severalfold) its ultimate fracture strain. The obtained results are interpreted on the basis of the analysis of changes in the structural state of the alloy. The proposed version of the kinetic theory of creep gives good agreement between the experimental and theoretical values of the principal characteristics of creep and long-term strength. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 5, pp. 98–104, September–October, 2008.