Disturbed State Model for Porous Saturated Materials

The widely used Terzaghi theory for deformation or consolidation in porous materials is based on the effective stress, a rather fictitious quantity, carried by the soil skeleton through the particle contact area, which is assumed to be negligible. This note presents a new generalized model based on the disturbed state concept, in which the average or weighted stress carried by the soil skeleton and fluid is defined on the basis of the change in contact area during deformation, that can be proportional to quantities such as the void ratio. A simple problem is solved in which the predictions from the proposed model and Terzaghi theory are compared. The proposed model has potential application as a general procedure for deformation in porous materials.     

Densification of iron compacts with various initial porosities under hydrostatic pressure

This study evaluated the effects of hydrostatic pressures up to 1104 MPa on densification of porous iron containing 0.3–11.1% porosity. For the porosities studied, densification as a result of pressurization increased with hydrostatic pressure and initial porosity. The 0.3% porosity iron was the only one whose density did not increase with pressurization up to 1104MPa. Current deformation models of ductile porous materials based on Gurson's yield criterion and rigid-plastic FEM analysis predicted much faster densification with pressurization than observed for porosity contents of 6.2% or less. A reason proposed for this behavior is the omission in the models of an internal pressure which builds up in the pores during the compaction process. A modification is introduced to Gurson's model to take account of internal pressure effects. The modified model exhibited excellent agreement with the experimental observations and provides a constitutive relation for the simulation of compaction and forming processes of P/M parts.     

Moiré method of the stress-strain state of sintered porous blanks in stamping

Conclusions It is demonstrated that the Moiré method can be successfully employed for studying the stress-strain state produced in sintered porous materials by plastic working. The strained state in the stamping of impressions with a flat cylindrical punch in a porous solid is characterized by the existence of two impeded deformation zones (under the punch and at the bottom of the blank) and a nonuniform distribution of displacement rates of points in the solid, deformation rates, and deformation rate intensities H_i on a meridional section. With decreasing starting density all these phenomena become less pronounced, and at a starting density of 60% the impeded deformation zones practically vanish. The distribution of stresses on a specimen section in the initial stage of stamping an impression is characterized-by a marked nonuniformity. The nonuniformity of stress distribution diminishes with decreasing starting specimen density and on passing from upper to lower (bottom) specimen layers. Experimental contact normal and tangential stress distribution curves have enabled deforming loads to be calculated and the locations of tangential stress maxima to be determined. It has been established that tangential stresses have their maxima at the punch corners, which accounts for the increased wear of the punch edge. With increasing starting specimen density the deforming load in the stamping of an impression sharply grows. Calculated values of deforming load, Pcalc, are in good agreement with experimentally determined values, P_exp.Translated from Poroshkovaya Metallurgiya, No. 10(214), pp. 7–13, October, 1980.     

PIMSIM: optimisation of powder injection moulding using advanced moulding simulations

Abstract

The present state of hipping modelling is briefly reviewed using the principles of densification theory and plastic deformation theory for porous materials on the basis of a macro- and microscopic approach. The features of these two approaches are discussed. The constitutive equation for a porous compact relating the strains and stresses (macroscopic approach) is modified by incorporating the rate equations for densification mechanisms (microscopic approach). A new modified constitutive equation is then derived which combines the advantages of both approaches. Based on this equation, the hipping process can be simulated. The density and shape change of a porous compact during densification or deformation processes under conditions of either isostatic or nonisostatic pressure can be predicted. PM/0645     

Process and compressive properties of porous nickel materials

Abstract

Compressive properties are investigated for the porous Ni materials processing by innovated powder metallurgical (PM) method. The porous Ni materials first show a short elastic region, then a long and oblique stress yield region within the strain range of about 10–50%, and finally, a densification region where the stress increases rapidly.     

The effects of triaxial stress on void growth and yield equations of power-hardening porous materials

In engineering applications, especially for ductile fracture of materials, nucleation, growth and coalescence of voids have often been observed. Currently there is an increase in interest for the effects of voids on the behaviour of engineering materials. In this paper, by the method of combining micro- and macro-parameters, the effects of triaxial stress on the rates of void growth and yield equations are presented for porous materials with power-hardening. The relations between triaxial stress and the rates of void growth for different n-values and yield equations with different n-values and void volume fractions are discussed. Following results have been obtained: For a porous material with power-hardening, the yield equation can be approximately expressed by an elliptical equation in equivalent stress and triaxial stress. Both the long half-axis and the short half-axis of the elliptical equation are functions of the void volume fraction for a given hardening exponent. The triaxial stress has a strong effect on the growth rates of voids. For linear hardening materials, the relation between the growth rate of voids and the triaxial stress is linear. For elastic/perfectly plastic materials with a small void volume fraction, the growth rate of voids can be described in relation to the triaxial stress with an exponential function. The results from this paper are compared with theoretical results from other researchers for elastic/perfectly plastic materials. A good agreement is shown.     

可压缩纯钼粉末烧结材料的塑性变形行为及影响因素

基于单轴压缩实验,研究纯钼粉末烧结材料的塑性变形行为及其影响因素。结果表明:可压缩纯钼粉末烧结材料的塑性变形行为对初始相对密度、温度和应变速率的变化相当敏感,其流动应力随应变速率的增加而增加,随温度的升高而减小;高温条件下材料对应变速率不太敏感,但初始相对密度在低温状况下对流动应力的影响更甚;对压缩后试样的微观组织分析显示:初始平均粒径为44.0μm的粗大等轴晶组织经过约35%的单轴压缩后,其中心主变形区域得到平均粒径为1.45μm完全致密的超细晶组织;初始相对密度越大,材料屈服强度越低,出现破裂的时间越早;其硬度增加速率对温度变化不敏感,而提高温度则有利于降低屈服强度。     

Methods of evaluating processing ductility in pressure treatment powder metals. II. Fracture criteria taking into account the stress state

Conclusions In addition to the parameter of the stress state, the ductility of the porous metals is strongly effected by the initial porosity, dimensions, in the form of the pores, and the condition of interparticle contacts. These parameters must be reflected in the fracture criterion.In the literature dealing with the fracture of porous materials in hot deformation, the principal criterion used in this case is that proposed by Kh. A. Kun which is based on the critical ratio of the main strains on the surface of the processed material. However, this criterion does not make it possible to predict internal fracture and does not take into account the loading history under the parameter of the stressed state.In the approach to predicting the failure of a porous blank, based on the equation proposed by M. Oyane, the loading history, the effect of the stress state and the porosity of the material are taken into account. The criterion does not take into account the effect of the form of pores and of the state of interparticle contacts.By taking into account the structural parameters in the ductility theory of porous bodies, proposed in [9], it is possible to predict the moment of failure. However, the method of determining the coefficient which takes into account the structural parameters has not as yet been developed so that it is difficult to apply the approach in practice.Analysis of the state of work in the area of processing ductility of porous metals shows that at present there are no sufficiently reliable criteria of the fracture of porous metals in plastic deformation which would take into account all factors affecting the ductility and would be suitable for use in practice. This should be the subject of further investigations.Translated from Poroshkovaya Metallurgiya, No. 9(345), pp. 10–14,September, 1991.     

Use of equations of the theory of plasticity of a porous solid for determining stresses in steady-state processes of plastic working of P/M materials

Conclusions A model of a plastic porous solid is proposed based on Beltrami's hypothesis concerning the transition to the plastic state, and equations are derived relating stresses to deformation rates. A method is described, based on the use of coordinate grids for finding deformation rate fields and of equations obtained in this work for the plastic flow of a porous solid, enabling stresses to be determined in steady-state processes of plastic working of P/M materials. The results are presented of a calculation, by this method, of stresses generated in the plastic broaching of holes in porous bushings from PZh2M2 iron powder.Translated from Poroshkovaya Metallurgiya, No. 6(210), pp. 15–21, June, 1980.     

Some features of the shape memory effect in a porous nickel-titanium material

Conclusions The shape memory effect exhibited by porous materials accounts for the volume memory characterizing porous bodies. Under conditions of a volume stressed state, porous sintered titanium nickelide can be deformed with densification without rupture to high degrees of deformation. The degree of completeness of shape recovery achieved during heating after deformation is less for porous than for nonporous titanium nickelide. This is linked with a heterogeneous character of deformation of a porous body and with the appearance in its volume of local zones characterized by high degrees of deformation, exceeding the reverse deformation reserve of the material, which lower the degree of completeness of shape recovery. With increasing starting porosity, the degree of completeness of shape recovery by titanium nickelide grows (at any given degree of prior macrodeformation). The degree of reversible deformation during the recovery of high-porosity titanium nickelide is not less than that of the intermetallic compound in the nonporous state, and the range of permissible degrees of prior macroscopic deformation for porous materials is much greater, which widens scope for the processing and application of these materials.Translated from Poroshkovaya Metallurgiya, No. 12(228), pp. 41–45, December, 1981.     

Simulating the compaction of layered porous billets

An ideal rigid-plastic porous body is used as a rheological model to develop a mathematical model describing a closed matrix compacted by the axial force of porous two-layer cylindrical axisymmetric billets with different geometry, porosity of the layers, and yield stress of the base material for each layer. It is shown that the compaction rate of two-layer porous billets under deformation is determined by the combination of their parameters such as the yield stress of the base material, initial porosity, and thickness. __________ Translated from Poroshkovaya Metallurgiya, Vol. 46, No. 5–6 (455), pp. 16–21, 2007.     

Mechanical properties of spinodally decomposed Fe-30 wt% Cr alloys: Yield strength and aging embrittlement

The age-hardening due to spinodal decomposition in Fe-30 wt% Cr alloys was studied. The yield stress was measured using monotonic tensile tests over a temperature range from 77 to 473 K. The observed incremental yield stress was found to be essentially test temperature independent, increasing substantially with increasing aging time as long as deformation occurs by a slip dominant mode. TEM observation of these test samples showed many dislocation pile-ups for aged materials while as-quenched materials exhibited a homogeneous dislocation distribution. The composition profile and consequent internal stress field due to isotropic decomposition were simulated using Cahn's multi-wave method. The results of this model were then used to estimate the yield stress for such an isotropic decomposition. Theory and experiment were compared using estimates of the extent of decomposition derived from detailed analyses of small angle neutron scattering (SANS). The results indicated that the misfit effect due to the coherent internal stress field is the dominant mechanism responsible for the observed age hardening. Experimental observations are consistent with a model for aging embrittlement which attributes the origin of twinning deformation to a Cr-rich second phase with Cr concentration greater than some critical value.     

The effect of hydrostatic pressure on the deformation behavior of maraging and HY-80 steels and its implications for plasticity theory

Earlier results showed that the difference between the tensile and compressive strengths of tempered martensites is primarily a manifestation of the general pressure dependence of flow stress in these materials. However, the same results also showed that the volume expansion after deformation was much smaller than that predicted by the normality flow rule of plasticity theory for materials with such pressure dependence. Additional results now obtained on maraging and HY-80 steels support these conclusions. The results for all these materials exhibit a strong, but not perfect, correlation between pressure dependence, yield stress, and volume expansion. The volume expansion, however, which is believed to result primarily from the generation of new dislocations, is very small and does not appear to be essential to the pressure dependence. Most of the pressure dependence, the portion responsible for the discrepancy with the normality flow rule, may be an effect on dislocation motion. The results suggest that an appropriate plasticity model would be one in which the octahedral shear yield stress is linearly dependent on the mean pressure, but the volume change is negligible in violation of the normality flow rule. Such a model has been proposed previously for the plastic deformation of soils. However, unlike that model, the present theory includes strain hardening.      

Evaluation of the Kinetics of Dynamic Recovery in AISI 321 Austenitic Stainless Steel Using Hot Flow Curves

The trend in the variations of the flow stress, obtained in the hot flow curves of materials, reflects the type of microstructural changes that occur during hot deformation. It is also possible to evaluate the kinetics of the relevant microstructural events directly from flow stress data. In the present study, a method for obtaining the kinetics of dynamic recovery from hot deformation flow curves has been proposed and carried out to evaluate the fraction of dynamic recovery in AISI 321 austenitic stainless steel during hot compression deformation in the temperature range of 800–950 °C. Results show that the rate of dynamic recovery is considerably increased by increasing strain rate. It has also been concluded, that the effect of deformation temperature on the kinetics of dynamic recovery is insignificant compared to the effect of strain rate. The flow behavior in a high temperature deformation reflects the type of microstructural changes that occur during deformation and is also possible to evaluate the kinetics of the relevant microstructural events directly from flow curve data. In the present study, a method to evaluate the fraction of dynamic recovery in AISI 321 austenitic stainless steel during hot compression in the temperature range of 800–950 °C has been proposed and carried out. Results indicate that the dynamic recovery process is considerably increased by increasing the strain rate and temperature.     

Numerical Modeling of the Compaction of Powder Articles of Complex Shape in Rigid Dies: Effect of Pressing Method on Density Distribution. 1. Mechanical Model of Powder Densification

A theory of plasticity of a porous body was formulated taking into account the specifics of powder behavior under pressing. The proposed model of the material under compression is one-parameter with all functions depending on the current density. In order to determine the parameters of the model, use was made of the equilibrium density attained during the compression of an unbonded powder body, that value of density beyond which further deformation is not accompanied by volume change. Methods for determining the material parameters of the model are described.     

The deformability of porous sintered materials in tension

Summary Formulas are derived for evaluating the deformation of porous sintered materials, taking into account the properties of the dense materials, the variation in the number of pores in various specimen cross sections, pore shape, and the loosening of materials during loading. The formulas obtained for the total strain, residual strain after fracture, and the limit of proportionality are compared with experimental data. Good agreement between experimental and calculated data was found.     

Effect of test conditions on the resistance of sintered strip to deformation

Conclusions It has been established that, in the deformation of sintered strip materials at h₀/b<1 and in the presence of lubricant on the contact surface, their resistance to deformation apparently tends to the variable yield stress _s, which in turn is a function of the degree of deformation . This is due to the fact that the pores and irregularities on the contact surface are capable of maintaining a boundary lubricant layer between the pressing tool (punch) and the specimen. Thus, the method of determination of the variable yield stress of dense specimens, in which the latter are swaged with flat, parallel punches, is suitable also, as confirmed by experimental data, for the determination of this parameter in the deformation of sintered strip materials.Translated from Poroshkovaya Metallurgiya, No. 9 (141), pp. 11–18, September, 1974.     

The effect of hydrostatic pressure on the deformation behavior of maraging and HY-80 steels and its implications for plasticity theory

Earlier results showed that the difference between the tensile and compressive strengths of tempered martensites is primarily a manifestation of the general pressure dependence of flow stress in these materials. However, the same results also showed that the volume expansion after deformation was much smaller than that predicted by the normality flow rule of plasticity theory for materials with such pressure dependence. Additional results now obtained on maraging and HY-80 steels support these conclusions. The results for all these materials exhibit a strong, but not perfect, correlation between pressure dependence, yield stress, and volume expansion. The volume expansion, however, which is believed to result primarily from the generation of new dislocations, is very small and does not appear to be essential to the pressure dependence. Most of the pressure dependence, the portion responsible for the discrepancy with the normality flow rule, may be an effect on dislocation motion. The results suggest that an appropriate plasticity model would be one in which the octahedral shear yield stress is linearly dependent on the mean pressure, but the volume change is negligible in violation of the normality flow rule. Such a model has been proposed previously for the plastic deformation of soils. However, unlike that model, the present theory includes strain hardening.     

Effect of porosity on the ductility and ductile failure mechanism of powder iron

Conclusions Formation of the ductility characteristics of the powder materials based on iron is associated with the transformation of the porous structure during deformation. The model proposed by Gerland [1] for materials with particles describes accurately the behavior of the material containing pores and links the true strain to fracture with porosity.The experimental dependence e_r=F(O) explains satisfactorily the formation of certain important processing characteristics of the material, such as cracking resistance and impact toughness. Since the yield stress of the material produced from various powders differs only slightly in a wide range of porosity, the main contribution to formation of cracking resistance and impact thoughness comes from the true strain to fracture (e_r).The difference in the content of the second phase particles in the iron powders of variousggrades leads to differences in the e_r values for the dense states; e_r decreases with increasing porosity. Thus, the high values of the impact toughness for the materials produced from WPL-200 and O Cher MK powders are explained by the low content of the second phase particles (1–2%) in comparison with the other materials, where the volume fraction of the particles was 3–5%.Translated from Poroshkovaya Metallurgiya, No. 10(298), pp. 90–96, October, 1987.     

Strain hardening during low temperature creep of 304 stainless steel

A study has been done of the strain hardening of 304 stainless steel during low temperature creep. Hardening is measured by additional loading (above the creep stress) after various creep times. Both the level and the shape of the strain versus stress curve are altered by creep; higher creep strain is linked to a higher offset yield stress and to a longer inelastic transient during the early stages of deformation during reloading. A theory is described in which the mobile dislocation density is determined by a competition between stress rate dependent injection and velocity dependent trapping. This theory predicts both the creep curve and the hardening effects of creep with good quantitative accuracy.