Effective Strain Rate Research Articles

Fatigue Analysis of Forged Aerospace Components Based on Micro Structural Parameters

With the objective of creating a simulation model for the lifetime calculation of forged aerospace components it is necessary to clarify the damage mechanisms in the materials used. This has been researched for the Ni-base alloy Inconel 718 by varying the forging parameter effective plastic strain rate, which is realised by using three types of equipment: hydraulic press, screw press and hammer. Specimens processed at the screw press show the highest lifetime by keeping all other forging parameters unvaried. Micro structural investigations show that the amount and morphology of dominant as-large-as grains play a important role. This methodology is currently investigated for Ti-6Al-4V. Lifetime tests show that besides effective strain and anisotropy the influence of morphology is important. As soon as the model status allows lifetime analyses the thermo-mechanical process (forging and heat treatment) can be developed depending on the desired lifetime specifications in order to realise an interdisciplinary lifetime optimisation of forgings. A further aim is the use of basic coherences of safe-life and fail-safe approaches in the low and high cycle fatigue region in order to reasonable handle with flaws and defects at the edge layer.

Failure of Dynamically Loaded Thermoelastoviscoplastic Rectangular Plate

The initiation and propagation of a crack and an adiabatic shear band in three-dimensional finite coupled thermomechanical deformations of a homogeneous and isotropic thermoelastoviscoplastic rectangular 4340 steel plate containing a centrally located through-the-thickness elliptic void and deformed in simple tension are analyzed numerically by using the finite element computer code DYNA3D. Initially, the major and the minor axes of the elliptic void coincide with the centroidal axes of the plate. An element is assumed to have failed when the damage parameter defined in terms of histories of the effective plastic strain, the effective plastic strain rate, the triaxiality factor, and the temperature at its centroid equals one; an adiabatic shear band initiates at a point when the effective plastic strain there equals one, while the material point is deforming plastically and deformations of the surrounding material are inhomogeneous. It is found that the ratio R of lengths of the two principal axes of the void significantly influences when and where a crack and an adiabatic shear band initiate and which one initiates first They usually originate from a point on the surface of the elliptic void which is also on the midsurface of the plate, and they propagate faster in the thickness direction. An adiabatic shear band initiates sooner in the three-dimensional simulations than when displacements in the thickness direction are constrained to vanish. The crack tip follows a zigzag path that does not lie in one plane.

Mechanical behavior of a superalloy with a rafted microstructure: In situ evaluation of the effective stresses and plastic strain rates of each phase

The elastic strain of both phases of a superalloy are measured by high-resolution in situ diffraction experiments done at 1070 °C, under variable stress from 0 to 300 MPa, on a specimen with a raft microstructure. The Young modulus can be evaluated, and the stresses and strain rates of both phases can then be calculated with a good precision. Between the pre-strain stress and the maximum stress, the effective stress within the γ phase remains at a constant level, just enough to allow dislocation glide within the rafts.

A model for an adaptable axisymmetric extrusion die with a bearing length

Abstract The adaptable design method uses upper bound models to determine die shapes that meet specified criteria, such as minimizing distortion in the product. This method has been developed for the axisymmetric extrusion process. In order to extend the methodology to the three-dimensional extrusion of a non-axisymmetric shape, the deformation zone in the upper bound model would need to be extended into the bearing region of the extrusion die. The necessary equations and conditions needed to make such an extension are presented in this paper. Finite element modeling (FEM) is used to compare the results of extrusion through dies designed by the adaptable die design method, for a model with the deformation zone extended into the bearing region, to a model without such an extension. The results indicate that the upper bound model incorporating a bearing length provides a realistic flow field. The results also demonstrate that the upper bound model can be used to analyze a multi-sectioned die, so long as: (1) the die surface and first derivative of the surface are continuous between sections, and (2) calculation of the internal power of deformation is made for each section separately. The results provide further support for the findings that the average effective strain and the volumetric effective strain rate deviation are robust criteria, which can be used to determine optimal adaptable die shapes with an upper bound model.

Thermomechanical instability analysis of inhomogeneous deformation in amorphous alloys

Recent experiments have shown that inhomogeneous deformation in amorphous alloys critically depends on the environmental temperature and the applied strain rate, and that the temperature field inside the shear-band can rise up to the glass transition temperature. A free-volume-based, thermo-viscoplastic constitutive law is developed in which the thermal transport equation includes contributions from the heating from plastic work and the heat conduction. For homogeneous deformation, the instantaneous temperature rise during the strain softening stage can lead to thermal softening and promote the initiation of shear bands. A linear stability analysis is carried out to examine the conditions for the unstable growth of temperature fluctuations. It is found out that the short-wavelength fluctuations, the amplitudes of which would decay at low strain rate and moderately high environmental temperature (but still much lower than the glass transition temperature), become unstable at high strain rate and low temperature, so that the resulting shear-band spacing will be shorter. A deformation mechanism map is constructed to delineate this transition of inhomogeneous deformation from coarse to fine shear-band arrangements. The theoretical results agree well with a nanoindentation experiment where there is varying applied strain rate and environmental temperature and with a microindentation experiment in which the evolution of the effective strain rate during loading influences the spatial distribution of the shear-band spacing observed using the bonded interface technique.

Finite Element Simulation of Magnesium Extrusion to Manufacture a Cross-Shaped Profile

At present, a fundamental knowledge of the thermal and mechanical interactions occurring during the extrusion of magnesium is lacking. This acts as a serious technological barrier to the cost-effective manufacturing of lightweight magnesium alloy profiles. In the present research, a three-dimensional finite element (FE) simulation of extrusion to produce a magnesium alloy profile with a cross shape was carried out as an efficient means to gain this understanding. It revealed the redistribution of temperatures in the billet throughout the process from the transient state to the steady state, the formation of the deformation zone and dead metal zone, and varying fields of effective stress, effective strain, effective strain rate, and temperature close to the die orifice. The predicted extrudate temperature and extrusion pressure were compared with experimental measurements. The key to controlling the extrudate temperature and extrusion process was found to lie in the capabilities of predicting the temperature evolution during transient extrusion, as affected by extrusion conditions. The relationship between ram speed and the extrudate temperature increase from the initial billet temperature was established and experimentally validated.

Adaptive rigid-plastic meshless Galerkin method and its application in analysis of extrusion processes

Under the hypothesis of the rigid-plastic material,specific efforts are placed on the deve-lopments of the key simulation techniques of the meshless Galerkin method because of the complexity of the deformation process as well as the generality and atomization of the simulation procedures for non-steady state large deformation plastic processes,therefore,an adaptive rigid meshless Galerkin method is developed. The influence domain control method is used in the least square approximation by dynamic evaluation of the magnitude of the influence domain and the effective control of the amount and the positions of the points in the least square approximation in order to improve approxi-mation precision. The amount of the Gauss integration points in the discrete domain is maintained in a considerable magnitude in order to ensure the integration precision in the discrete domain. The length of the frictional boundary of the plastic deformation process may be getting longer when its deforma-tion is getting severe. Thus,the densities of the boundary points of some places get lower. The adap-tive boundary points setting method is employed to improve the approximation precision of the boundary points and enhance the constraint of the boundary condition by adaptive control of boun-dary point density. Some typical extrusion processes are analyzed,detail simulation results such as the deformation field,velocity field,effective strain field,effective strain rate field,the volume loss curve and load-stroke curve are obtained. The effectiveness of the method developed is demonstrated and the precision of the meshless simulation is proved by overall comparison with the results obtained by using the commercial software deform.

Inner-product of strain rate vector through direction cosine in coordinates for disk forging

A new linear integration for plastic power was proposed. The effective strain rate for disk forging with bulge was expressed in terms of two-dimensional strain rate vector, and then its direction cosines were determined by the ratio of coordinate increments. Furthermore, inner-product of the vector for plastic power was term integrated by term and summed. Thereafter, through a formula for determination of bulge an analytical solution of stress effective factor was obtained. Finally, through compression tests, the calculated results of above formula were compared with those of Avitzur's approximate solution and total indicator readings of the testing machine. It is indicated that the calculated compression forces are basically in agreement with the measured ones if the pass reduction is less than 13.35%. However, when the reduction gets up to 25.34% and 33.12%, the corresponding errors between the calculated and measured results also get up to 6% and 13.5%, respectively.

Effective Stresses and Plastic Strain Rates in a Superalloy: a High Temperature In Situ Study by Synchrotron X-Ray TCD

Variations in the lattice parameters of γ and γ' phases perpendicular to the [001] tensile axis were recorded in situ at ~10 minutes intervals using the Triple Axis Diffractometer of the High Energy (ID15) beamline at ESRF. Testing was carried out on an AM1 superalloy specimen with a raft microstructure at high temperature (1072°C) under load steps between 0 MPa and 300 MPa. These data were used to evaluate the Young modulus and the effective (Von Mises) stresses within the γ' rafts and γ corridors, as well the average plastic strain rates of each phase. The recorded stress data scatter was within the MPa range, and should be good enough to probe the elementary mechanisms of plasticity.

Grain structure evolution in a 6061 aluminum alloy during hot torsion

The grain structure development of 6061 aluminum alloys deformed at elevated temperatures in torsion is presented here and related to industrial processing scenarios. Samples of a 6061 aluminum alloy representing two variations in chemistry have been studied at different values of effective strain, ɛ eff., strain rate, ε ˙ , and temperature, T. Rapid quenching techniques were implemented to ensure preservation of the deformed microstructure after deformation ceased. It was determined that at effective torsion strains greater than 2.5, a fine, equiaxed grain structure develops and may be related to a type of dynamic recrystallization (DRX). The final grain size increases with increasing deformation temperature.

NUMERICAL MODELLING OF EXTRUSION PROCESS IN SUPERPLASTIC FLOW RANGE

The results of numerical modeling of direct and indirect extrusion process of a model alloy of high strain-rate sensitivity at room temperature, Sn38Pb, are presented. The studies were carried out for three values of die angle, three temperatures, four ram speed values, two values of extrusion coefficient and two values of friction factor. Effect of extrusion process parameters on distribution of effective strain, effective strain rate in extruded bar and extrusion load was estimated.

The coupling thermal–mechanical and microstructural model for the FEM simulation of cross wedge rolling

The microstructural evolution models on AISI 5140 were obtained using the Gleeble-3500 thermo-mechanical simulator. Simulation on the cross wedge rolling (CWR) process has been carried out on the platform of finite element software DEFROM-3D with thermo-mechanic and microstructural evolution coupled. And distributions of the different field-variables during the whole rolling process from the knifing, guiding, stretching to sizing stage, such as effective strain, effective strain rate and temperature, were obtained. Meanwhile, three-dimensional (3D) distribution of austenite grain size of workpiece was also achieved. It is significant to understand the net-shaped mechanism and optimize CWR technology.

Combined surface density concepts for dense spray combustion

Concepts of surface density are exploited to model the coupled processes of atomization, vaporization, and combustion in turbulent jet flames formed by cryogenic propellants. An Eulerian framework is used to describe the two-phase flow formed by a coaxial injector fed by liquid oxygen and gaseous hydrogen. A transport equation for the density of the liquid interface represents the jet break-up, subsequent atomization, and space–time evolution of the liquid surface area which combined with a local description of the vaporization flux provides the volumetric source of gaseous oxygen. Subcritical and transcritical conditions are successively considered. Another transport equation for the flame surface density is then used to evaluate the mean reaction rate per unit volume. This reaction rate depends on an effective strain rate and on operating parameters such as the mean pressure prevailing in the combustion chamber. A simple analysis based on the fast chemistry limit indicates that the local rate of reaction varies like the square root of pressure and strain rate. A computational model combining these various elements is established. Calculated cryogenic flame structures are compared to recent experimental data corresponding to different gas to liquid momentum flux ratios and chamber pressures. The mean reaction rate spatial maps are in agreement with experimental OH light emission images which are used to locate the chemical reaction regions. Parametric studies indicate how the liquid or transcritical phase evolution modifies the flame pattern.

Effect of thermal treatments on the yielding of polycarbonate

AbstractTwo different thermal treatments were applied to polycarbonate (PC) in terms of slow cooling (annealed samples) after a thermal treatment at a temperature above the glass‐transition temperature or abrupt cooling in a liquid‐nitrogen environment (quenched samples). Tensile and compression experiments were performed on the two types of samples at three different effective strain rates. A viscoplastic model based on the fundamental assumptions of the Eyring model and on a kinematic formulation, which separated the viscoelastic and plastic strain, developed in previous works, was used to describe the yield and postyield behavior of thermally treated PC. The different thermal treatments affected the parameters of the material microstructure. A satisfactory agreement between the experimental data and calculated results was found. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 796–805, 2005

A viscoplastic strain gradient analysis of materials with voids or inclusions

A finite strain viscoplastic nonlocal plasticity model is formulated and implemented numerically within a finite element framework. The model is a viscoplastic generalisation of the finite strain generalisation by Niordson and Redanz (2004) [Journal of the Mechanics and Physics of Solids 52, 2431–2454] of the strain gradient plasticity theory proposed by Fleck and Hutchinson (2001) [Journal of the Mechanics and Physics of Solids 49, 2245–2271]. The formulation is based on a viscoplastic potential that enables the formulation of the model so that it reduces to the strain gradient plasticity theory in the absence of viscous effects. The numerical implementation uses increments of the effective plastic strain rate as degrees of freedom in addition to increments of displacement. To illustrate predictions of the model, results are presented for materials containing either voids or rigid inclusions. It is shown how the model predicts increased overall yield strength, as compared to conventional predictions, when voids or inclusions are in the micron range. Furthermore, it is illustrated how the higher order boundary conditions at the interface between inclusions and matrix material are important to the overall yield strength as well as the material hardening.

Strain rate effect on in-plane shear strength of unidirectional polymeric composites

The strain rate effect on the in-plane shear strength of unidirectional composites was investigated. Off-axis S2/8552 glass epoxy block specimens were employed to produce in-plane shear failure. In order to determine the strain rate effect, specimens were tested in compression at various strain rates. For strain rates less than 1/s, experiments were conducted on an MTS machine. For higher strain rates, they were performed using a Hopkinson pressure bar. Experimental observations indicated that, for composite specimens with off-axis angles less than 10°, fiber microbuckling is the dominant failure mechanism. However, for the specimens with off-axis angles between 15° and 45°, in-plane sharing is the major failure mode. If the off-axis angle is greater than 45°, out of plane shear failure would take place. Only the in-plane shear failure mechanism was concerned in this study. The shear strain rate was obtained from the uniaxial strain rate by relating the effective plastic strain rate to the plastic shear strain rate with the aid of a viscoplasticity model. Through coordinate transformation law, the uniaxial failure stresses were then converted to a plot of shear stress versus transverse normal stress from which the shear strength in the absence of transverse normal stress ( σ 22 = 0) was obtained. Experimental results showed that the shear strength of the composite is quite sensitive to strain rate and the shear strength increases as strain rate increases. In contrast, the shear failure strain decreases as strain rate increases.

Behaviour of Cu-Zn alloys in high speed shear tests and in chip formation processes

In order to assess the material behaviour of brass during metal cutting processes, dynamic shear tests are carried out with effective strain rates between 1 × 10 −3 and 2 × 10 5 s −1. The high strain rates are realized in hat-shaped shear specimens using a split Hopkinson compression-bar configuration. Different α- and α/β-brasses with and without lead are tested in annealed and strain-hardened condition. In the range of high stain rate, the material behaviour is governed mainly by two contrary effects: first, the adiabatic character behaviour of the high-speed deformation process, which promotes deformation localization; and second, the increased strain-rate sensitivity, which has a stabilizing effect on the deformation process and reduces the strain concentration. Both the effective strain at fracture and the deformation work per unit volume are considered as indicators for the formation of continuous chips during metal cutting. Beyond 10 4 s −1, both values are approximately proportional to the strain rate. The dependence of chip fragmentation on main cutting parameters is explained by these functions.

Numerical simulation of finish hard turning for AISI H13 die steel

A coupled thermo-mechanical model of plane-strain orthogonal turning of hardened steel was presented. In general, the flow stress models used in computer simulation of machining processes are a function of effective strain, effective strain rate and temperature developed during the cutting process. However, these models do not adequately describe the material behavior in hard machining, where the workpiece material is machined in its hardened condition. This hardness modifies the strength and work hardening characteristics of the material being cut. So, the flow stress of the work-material was taken with literature [H. Yan, J. Hua, R. Shivpuri, Development of flow stress model for hard machining of AISI H13 work tool steel. The Fourth International Conference on Physical and Numerical Simulation of Materials Processing, Shanghui in China, 2004, p. 5] in order to take into account the effect of the large strain, strain-rate, temperature and initial workpiece hardness. Then a series of numerical simulations had been done to investigate the effect of machining parameters on the machinability of hardened steel AISI H13 in finish turning process. The results obtained are helpful for optimizing process parameters and improving the design of cutting inserts in finish turning of hardened steel AISI H13.

Locally refined tetrahedral mesh generation based on advancing front technique with optimization and smoothing scheme

AbstractIn this paper, a locally refined tetrahedral mesh generation algorithm based on advancing front technique using optimization scheme with a non‐uniform trial height has been developed for three dimensional forming simulations to improve the quality of the local mesh system and computational efficiency. To generate locally refined surface elements, the refinement region was identified by checking the local effective strain rate and minimum interior angle of a surface element, respectively. In addition, a limiting value for the edge length of the tetrahedron was introduced to avoid generation of extremely small triangular surface elements. The developed scheme was applied for numerical simulations of indentation and spur gear and connecting rod forging. The computational results indicate that the currently developed algorithm was successful in generating better mesh system to finish numerical simulations with relatively shorter computation time compared to the previous scheme with a uniform trial height available in the literature. Copyright © 2004 John Wiley & Sons, Ltd.

Hot deformation of austenite and prediction of microstructure evolution of cross-wedge rolling

Abstract Constant strain rate compression tests were carried out on AISI 5140 using the Gleeble-3500 thermomechanical simulator. The mechanical behavior and the dynamic structure changes were investigated metallographically in the temperature range from 900 to 1100 °C and at the strain rate ranging from 0.1 to 10 s −1 . A dynamic recrystallized grain size model and a volume fraction model were presented as well as a diagram of dynamic microstructure state. The cross-wedge rolling process for shafts was simulated through establishing a theoretical model on the finite element software DEFORM. The distributions of the different field-variable, such as effective strain, effective strain rate and temperature, were obtained. Meanwhile, mean grain size distribution after rolling was presented in this paper.