Plastic Constraint Research Articles

The effect of interface diffusion and slip on the creep resistance of particulate composite materials

Reinforcements are known to increase the creep resistance of metal and intermetallic matrix composite materials. Experimental measurements at modest temperatures indicate that under a given applied strain rate the composite strength is higher than that of the matrix alone. However, at temperatures higher than approximately half of the melting temperature of the matrix, the composite strength is limited and in some cases the strengthening imparted by the reinforcements is completely lost. Diffusional relaxation and slip on the reinforcement-matrix interface are suggested as mechanisms responsible for the loss of strengthening. According to the proposed model, stress gradients caused by plastic constraint induce diffusional flow along the interface accompanied by slip of the matrix over the reinforcement. As a result the constraint tends to be relaxed and strengthening can be eliminated. The composite behavior is investigated by coupling the diffusion and slip along the interface with deformation of the matrix in the power law creep regime. A unit cell model is used in axial symmetry and the relevant boundary value problem is solved by the finite element method. Numerical results indicate that either diffusional relaxation or slip may knock down the creep resistance of the composite to levels even below the matrix strength.

Strength of mixtures of bainite and martensite

Recently published experimental data demonstrate that the strength of mixed microstructures of tempered bainite and martensite can peak at an intermediate volume fraction of martensite. In the present work, a quantitative interpretation of these observations is achieved by modelling the mechanical properties of bainite and martensite in their tempered states. It is found that the peak in the curve of the strength as a function of the volume fraction of martensite can be attributed to two factors. When bainite forms it enriches the residual austenite with carbon, so that the strength of the subsequent martensite increases. In addition, during its deformation, the strength of the bainite is enhanced via plastic constraint by the surrounding stronger martensite. Taking these effects into account, it is possible to predict accurately both the trends and the absolute values of published experimental data on the strength of mixed microstructures.MST/1901

The toughening of polyamide-6 by brominated poly(isobutylene- co- p-methylstyrene): fracture and toughening mechanisms

A study on the toughening of polyamide-6 (PA-6) with a new elastomeric modifier, brominated poly(isobutylene- co- p-methylstyrene) (BrXP-50), was conducted. Morphological analyses and mechanical tests were combined to evaluate the toughening mechanisms of modified PA-6 and the fracture mechanism of unmodified PA-6. We conclude that the fracture mechanism of unmodified PA-6 in the impact test is crazing-cracking under the dilatational stress created by the plastic constraint, while that of the BrXP-50 elastomer modified PA-6 is plastic tearing limited by the ultimate tensile strain. Cavitation of BrXP-50 elastomer particles occurred in the impact test, and is proposed as a controlling step in toughening: it relieves the plastic constraint so that the cracking process is postponed and additional plastic deformation can occur, leading to higher impact toughness.

Computational modeling of metal matrix composite materials—IV. Thermal deformations

The mechanical behavior of particulate reinforced metal matrix composites, in particular an SiC reinforced Al-3 wt% Cu model system, was analyzed numerically using the computational micromechanics approach. In this, the fourth and final article in a series, the microscale effects of thermo-mechanical processing is investigated in detail. Two ideal processes are considered. The first represents a simple quench and the second combines a high temperature compression, to simulate rolling or extrusion, with a quench. These processes, through applied deformation and thermal expansion mismatch, produce inhomogenous, and localized, stress and plastic strain fields in the composite microstructures. The structure of these residual fields can be related to reinforcement volume fraction and microstructural morphology. For the simple quench, volume average plastic strains are almost proportional to reinforcement volume fraction and there is a negligible morphological dependence. Large magnitude residual stress and strain fields, as well as large geometry changes, result from the second process. The effects of these processes on subsequent deformation behavior of composites for a selection of morphologies is investigated. Apart from almost doubling yield strains, the simple quench has relatively minor microscale and macroscale effects. The second process has a considerable effect on yield strength and introduces differences between tensile and compressive behavior on both the macroscale and microscale. Plastic constraint is an important mechanism. The physical relevance of these particular processing simulations, and the implications for modeling of microscale failure are discussed.

Fatigue and creep of a constrained metal wire

An experimental investigation has been conducted to examine the enhancement of toughness of composites due to crack bridging under creep and fatigue conditions. The model composite used for the study consists of a metal wire inside a thick-walled glass tube. It is found that the fatigue and the creep resistance of the constrained wire depends upon the failure mechanism. Compared with the unconstrained monolithic wire, the model composite shows greater fatigue and creep strengths due to plastic constraint. The failure stretch of the constrained wire is less for fatigue loading than for monotonic loading; the contribution to toughening is thus reduced under cyclic loading. The failure stretch in creep is dependent only upon the failure mechanism and not upon the applied stress level.

An improved collapse axis on the R6 FAD for combined tension and bending loading

Experimental and computational studies were made of a number of single edge notch (SEN) specimens loaded through eccentric pins with notch depth ratios 0.21 and 0.52. It was found that as the applied load was increased the formation of a plastic hinge mechanism caused the ligament to shift sideways and in turn alter the ratio of bending to tension loading. The two different assumptions, constant and variable bending to tension ratio, gave very different paths in the moment-load ( M-Q) space, and failure lines when plotted on the R6 Fracture Analysis Diagram (FAD). An improved expression for normalized load, Sr, for SEN geometries under a linear loading system was obtained by including a plastic constraint factor in the uncreacked lower bound solution. For the pin-loaded SEN specimens under a non-linear loading system, it was shown that Sr based on ‘true path lengths’ in the yield diagram gave a failure curve which was in good agreement with the R6 Rev3 solution.

Ｓｈａｌｌｏｗ Ｎｏｔｃｈ ＣＴＯＤ試験の意義 溶接継手の破壊性能評価のための靭性評価手法に関する考察

The use of CTOD bend specimen with a deep notch whose length is equal to the plate thickness is not always appropriate to obtain the toughness data applicable to fracture performance evaluation of weld joints. In this paper, HAZ-notched bend test and tension test have been conducted using specimens with different notch depth, which were extracted from a multipass weld joint of 30 mm thick high strength steel (TMCP type) with 460 MPa class yield point. The critical CTOD value at unstable fracture initiation obtained by the deep notch bend test was apparently smaller than that for the tension specimen. Fracture mode was also affected by the specimen type : Perfect cleavage fracture was dominant in the deep notch bend specimen, whereas unstable fracture preceded by a large amount of stable crack growth was observed in the tension specimen. Difference between CTOD results for the deep notch bend specimen and the tension specimen can be attributed to the crack tip constraint effect. The deep notch bend specimen exhibits significantly elevated crack tip stress and higher stress triaxiality compared to the tension specimen. By contrast, a shallow notch bend specimen showed a similar fracture behavior and critical CTOD value as the tension specimen. For the assessment of fracture resistance of welds by the CTOD bend test, the notch depth should be designed to simulate the plastic constraint expected in weldments.

Constraint of side-groove and its influence on fracture toughness parameter in Charpy-size specimens

The effect of a side-groove constraint on a pre-cracked Charpy-size specimen, and the influence of a side-groove on fracture toughness parameters are studied. The results indicate that when side-groove depth approaches a critical value, the maximum load toughness J m values are nearly coincident with the initiation toughness J i , values. The thickening action of the side-groove may be expressed by calculating the extra thickness of the specimen. For different materials the additional thickness due to the side-groove is distinct. When the side-groove depth is 33% of the specimen thickness the specimen obtains the maximum additional thickness. The side-groove constraint coefficient ( C) presented by this paper can quantitatively evaluate the level of plastic constraint at the crack tip, and explains the experimental results well.

Models for plastic constraint in brazed or diffusion-bonded joints between ceramic components

Slip line field theory and the upper bound theorem are used to analyze the problem of two monolithic ceramic components bonded by a ductile metal interlayer. The presence of even a small fraction of debonded region is shown to have a significant effect on the performance of the joint. The required integrity and dimensions of the interlayer material are then found, to obtain a particular load-carrying capacity.

The mechanical properties of Al alloys reinforced with continuous Al 2O 3 fibers

The mechanical properties of aluminum matrix composites unidirectionally reinforced with Al 2O 3 fibers have been measured and characterized in longitudinal and transverse tension, as well as in shear. The flow strengths in transverse tension and shear are found to exceed those of the matrices, although the ductilities are lower. The strengthening is generally consistent with the development of plastic constraint in the matrix around well-bonded fibers, subject to the in situ properties of the matrix being known from independent measurements. The properties in longitudinal tension are found to involve interactions between fibers, such that fiber bundle strengths are not achieved, even when a low strength, pure Al matrix is used. Instead, the strengths are consistent with a crack growth controlled failure mechanism, wherein the strength is governed by the resistance of the material to crack extension from failed fibers.

Palladium-zirconia diffusion bonds: Mechanical properties and interface reactions

High strength and toughness diffusion bonds have been fabricated using palladium foils between TZP zirconia blocks at temperatures above 1000°C in vacuum. Bonds fabricated below 1000°C in vacuum and under all conditions in air showed negligible strength. Strong, vacuum made bonds lost almost all their strength on annealing in air above 1000°C, anneals in vacuum also resulted in a decrease in bond strength but with a much less marked effect. PdZrO 2 interfaces have been characterised by cross-sectional TEM and a thin reaction zone identified. Microanalysis identified the presence of Pd, Zr and O in a ratio of approximately 30:52:18 in the reaction interlayer. This composition has a Pd:Zr ratio close to that of a steep eutectic in the PdZr binary system and evidence for the presence of a liquid phase at the PdZrO 2 interface during bonding is presented. The strength and toughness of the bonds are shown to be strongly dependent on the perfection of the bonded interface with the presence of a small fraction of voids causing a significant reduction in bond strength and toughness. Simple slip-line field methods are used to illustrate the influence of interface voids on the plastic constraint of bonded thin ductile layers.

き裂開閉口によるき裂先端付近の局所応力とひずみの変動およびき裂開閉口点の測定について

The local stress and strain in the vicinity of crack tip were calculated by means of a finite element method to examine the measuring method of crack closure points. The fatigue crack closure behavior affected the local stress σx of cracking direction much more than the local stress σy, of loading direction in the vicinity of crack tip. The diagram between the nominal stress σ representing cyclic loading and σx had some inflection points. One of them well coincided with the crack opening point. However, some undesirable inflection points due to plastic constraint or crack blunting etc. were also found on the σ-σx diagram. On the other hand, the diagram between σ and the local shear stress τ in the vicinity of crack tip was found to have clear inflection points related to the crack closure behavior. It is expected that the crack closure points can be measured easily with an adequate strain function in the vicinity of crack tip.

CTOD Estimates of surface cracked wide plates in bending—I. Finite element analysis

Three dimensional elastic-plastic finite element analysis of the surface cracked wide plate in bending was performed. Applied crack tip opening displacement (CTOD) extracted from the finite element nodal displacements showed a good correlation with the experimental results. The crack tip at the bottom of the surface crack was in plane strain accompanied by the high plastic constraint. Applied CTOD was estimated by the WI-CTOD design curve and compared with the finite element results. The conservatism of the CTOD design curve was highly dependent on the definition of applied strain and the crack geometries. For the surface crack with aspect ratio of 0.1, the applied CTOD was underestimated in the large scale yield range.

A mechanical and metallurgical approach to the characteristic brittle-to-ductile-transition temperature

Investigation of the brittle-to-ductile transition of mild steel was carried out. A representative temperature T pm was defined and the transitions for the fracture toughness and the crack arrest were discovered at T pm . On the basis of the features of cleavage fracture, the criterion for cleavage microcrack propagation across the grain boundary was established. By means of a simulation of cleavage fracture behaviour of the cracked bend specimen, the variation in the resistance to the microcrack propagation with temperature was revealed, and a sharp increase in the crack resistance because of the decrease in plastic constraint and increase in the effect of microcrack blunting at temperatures above T pm was demonstrated. The implication is that the transitions at T pm are actually the expressions of a change in the crack resistance and T pm is a temperature which marks the beginning of the great increase in the crack resistance. Moreover, T pm mainly depends on the property of material if the specimen meets a certain plastic constraint and hence the T pm can be used to describe the fracture behaviour of the steel at low temperatures.

Estimation of plastic constraint and local strain at the notch root for notched plates and bars.

Plastic constraint and local strain at the notch root for notched plates and bars were examined in the elastic-plastic and full plastic regions by FEM. By introducing the mean equivalent stress, σ(Mises), and the strain, e, at the minimum cross section, and the equivalent stress concentration factors, Kt, the results obtained in this study are summarized as follows: (1) The plastic constraint factor k defined by σ/σn was nearly constant under the wide range of deformations, and independent of the material constants. (2) The general yield stress σGY was derived based on the idea that the mean equivalent strain in the elastic state is almost equal to that in the plastic state. (3) The relationship between σ and e for σ≥σGY was approximately in accord with the constitutive equation of the materials and was e=Bσm for σ≤σGY. (4) The equivalent strain, e, at the notch root was simply estimated from e=Kt e.

Plane strain elastic-ideally plastic crack fields for mode I quasistatic growth at large-scale yielding—I. A new family of analytical solutions

I n an effort to extend the theoretical foundations for understanding and quantitatively describing stable plane strain tensile crack growth in ductile materials to large-scale and general yielding situations, we derive a new family of solutions for the near-tip stress and deformation fields of such growing cracks, within the most analytically tractable model of isotropic, incompressible, elastic-ideally plastic PrandtlReuss-Mises material. One limiting member of this new family is the previously-derived “modified Prandtl field” solution that is believed to apply under small-scale yielding conditions. We provide evidence that the present solution family, which involves a parameter that is unspecified by the near-tip analysis, may be able to describe growing crack fields for the entire range of yielding extent from small-scale through general yielding conditions in potentially arbitrary Mode I plane strain geometries. Except for the “modified Prandtl field” limiting case, all members of the new solution family exhibit: (i) singular straining in the “constant stress” plastic sector ahead of the growing crack tip as well as in the “centered fan” plastic sectors that lie above and below the growing tip; and (ii) completely continuous near-tip stress and velocity fields. While the solution family derived is the result of a leading-order (in distance, r, from the moving crack tip) asymptotic analysis of the continuum mechanical field equations, we extend this solution explicitly to large r within the region of principal plastic deformation, thereby elucidating the radial dependence of the stress field (not specified by a leading-order analysis in nonhardening materials), and providing a framework for assessing the influence of far-field boundary conditions (specimen geometry and loading) on near-tip fields. Also, the new solution family is shown to provide a natural, fundamentalsbased generalization, possibly to arbitrary yielding extent and plastic constraint level, of an existing successful well-contained-yielding ductile crack growth criterion.

Slip-line field solutions for three-point notch-bend specimens

The slip-line field solutions for three-point bend specimens are reviewed for both deep and shallow notches. Plastic constraint factors, hydrostatic stress at the notch root and rotation constant to enable the crack upp opening displacement to be determined are given for a wide range of notch geometries. These values can be used in the fracture analysis of low strength metal specimens.

Near-Threshold Fatigue Crack Growth Behavior for 316 Stainless Steel

Abstract Fatigue crack growth threshold behavior of Type 316 stainless steel was studied in air at 24°C to evaluate the effects of load-shedding rate and specimen geometry on ultra-low crack growth rates. Load-shedding rates greater than the maximum rate recommended in the proposed ASTM test procedure were found to have no substantial effect on the threshold behavior. At very low ΔK levels, crack growth rates were apparently dependent on environmental effects and the degree of plastic constraint.

Evaluation of Intergranular Fracture Initiation in Transition Region of Retired Steam Turbine Rotor Steel Using Small Specimens and the Acoustic Emission Technique

Abstract Fracture toughness tests were performed at 150°C in the transition region for a Cr-Mo-V steel using four different sizes of compact tension specimens and with the use of the acoustic emission (AE) technique. Two fracture toughness parameters were obtained to evaluate the intergranular mode fracture toughness: one is the critical fracture toughness of KJC calculated from Jc, the other is a fracture toughness of KJAE characterized by the onset of microscopic pop-in cracking determined by AE. The values of KJC and KJAE of the smaller specimens show a great deal of scatter. Combining the fractographic studies, the source of toughness scatter is discussed in terms of the loss of plastic constraint. The results show that the lower bound values of KJAE in the smaller specimen sizes are coincident with a valid fracture toughness, KIC(AE), of the large specimen. An accurate evaluation of the intergranular mode fracture toughness is also discussed.

EFFECT OF FATIGUE CRACK CLOSURE ON NEAR‐THRESHOLD CRACK RESISTANCE OF STRUCTURAL STEELS

Abstract— The present paper is an attempt to clarify conditions for plasticity‐induced and oxide‐induced crack closure as well as to evaluate the effect of crack closure on near‐threshold fatigue crack behaviour.The autocatalytic character of oxide formation at the crack tip has been elucidated in this study. An increase of plastic constraint at the crack tip is shown to intensify the fretting oxide formation process on the fracture surface and thus to cause an increase of the stress intensity factor range controlling the fatigue crack propagation rate. The proposed concept of stress state influence on crack closure allows us to explain the effect of specimen thickness on ΔKth.