Size Of Deformation Zone Research Articles

Influence of particle deformation zone (PDZ) size on dynamic recrystallization and precipitation behavior of SiCp/Mg-5Zn material during hot compression

The influence of particle deformation zone (PDZ) size on dynamic recrystallization (DRX) and precipitation behavior of SiCp/Mg-5Zn material was investigated through the hot compression. First, the microstructure and microhardness of matrix in PDZ were characterized for SiCp/Mg after compression at room temperature. Then, the microstructure evolution of SiCp/Mg-5Zn materials with different PDZ size was analyzed by optical microscopy (OM), scanning electron microscopy (SEM), electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM) after compressing different strains. The results show that a significant misorientation gradient was formed near the particle for SiCp/Mg after compression at room temperature, but which is smaller than that around the grain boundary. The addition of SiCp can promote DRX nucleation of Mg matrix, but the promotion effect of particles on DRX nucleation is less than that of grain boundaries for SiCp/Mg-5Zn material during the hot compression, which causes a decrease in the DRXed ratio of SiCp/Mg-5Zn material with increasing PDZ size. Moreover, the volume fraction and size of precipitated phase both decrease with increasing the PDZ size. The aim of this work is to provide a strategy to acquire Mg alloys with excellent mechanical performance by regulating the microstructure of Mg matrix.

Sensitivity analysis of a three-invariant plasticity model with different sampling algorithms

ABSTRACT A Sobol sensitivity analysis is employed to identify the importance of parameters in the three-invariant soil model (GeoModel) for finite element simulation. Three commonly used sampling techniques, namely, pseudo-random, quasi-random (QR), and Latin-hypercube sampling (LHS), are investigated to determine the efficiency of each sampling technique for sensitivity analysis and identify the critical parameters for the soil model. Among the sampling methods, LHS shows the best sampling uniformity and offers more stable results and faster convergence than other methods. The analysis results also show that Young’s modulus and the initial value for the shear-yield surface are the most critical parameters for the designed outputs, which quantitatively measure the maximum total deformation (MD), plastic deformation (PV), and plastic zone size (VY). The proposed sensitivity analysis framework in this study can be applied to finite element simulations of similar engineering and scientific problems for assessing model parameters’ influence.

Regularities of plastic deformation development in the crack tip vicinity

When determining the service life of cyclically loaded metal structures at the stage of fatigue crack development, an important role is played by the accuracy of assessing the plastic deformation zone size at the crack tip formed by the tensile overload. Within this zone, after reducing the load to the initial level, the fatigue crack development slows down. Despite the large number of studies in this area, none of the proposed dependencies is currently fully confirmed by experimental results in determining the plasticity zone size. The aim of the work is to assess the size of the plastic deformation zone formed by a single tensile overload. In the work of the finite element method for central-notch specimens and compact tension specimens, an analysis of the stress-strain state in the crack top vicinity is performed. As a calculation, a flat and three-dimensional model was used. Calculations are performed in the Ansys 14.0. Data on the mechanical properties of steels were used: St20, VSt3sp, 09G2S, 15G2SF. With increasing load, the plastic zone size in front of the crack tip was estimated, in the process of reduction, the distribution and length of the fields of residual compressive stresses and the size of the cyclic plastic zone were recorded, the length of which was also determined experimentally using strain gauges with a base of 0.5 mm. To assess the plastic zone size formed by a single tensile overload, a dependence is proposed that takes into account the patterns of plastic deformation development in the vicinity of the fatigue crack tip, and the results of the calculation agree well with the experimental data given in the literature. The obtained expression makes it possible to predict with greater reliability the development of fatigue cracks at variable load amplitudes.

Temperature dependent fatigue crack growth in electrical steel laminates with μm-thick epoxy layers

The effect of adhesive layer thickness on monotonic roll peel strength and fatigue crack-growth kinetics was investigated for electrical steel laminates with bond line thickness values ranging from 7 to 48 μm. Roll peel strength was increasing with epoxy layer thickness up to 20 μm. In contrast, roll peel strength was leveling at higher thickness values. The fatigue fracture mechanics approach in mode I delivered an equivalent ranking such as roll peel testing. However, energy-based fracture mechanics analysis was much more sensitive than monotonic roll peel testing, also at thicker bond lines. The different failure modes were correlated with the plastic deformation zone size developing at the propagating crack. In case of a constrained plastic zone, cohesive failure mainly within the epoxy layer was ascertained. In contrast, interfacial failure and interestingly also a better fatigue crack growth resistance was deduced for a weakly or non-constrained plastic zone. Regarding the temperature dependency, an enhanced fatigue crack resistance was obtained at 60 °C. At this temperature about 50 °C below the maximum of the loss factor of the epoxy adhesive, the effect of epoxy layer thickness was much smaller than at 23 °C. At testing temperatures slightly below or above the glass transition temperature, the fatigue crack propagation rate was a factor of 10 to 100 higher.

Collaborative Mining Sequence Optimization for Multiple Stopes under Intensive Mining

The optimization of a mining sequence not only reduces stress concentration in surrounding rock but also prevents underground debris flows, significantly improving safety. Firstly, the 870–898 m level of the eastern mining area in the Tiaoshuihe phosphate mine was divided into 25 ore blocks, and six different mining sequences were designed for this area. Then, it was calculated that five ore blocks must be processed simultaneously to reach the annual production output. The distances between the five simultaneously mined ore blocks will inevitably affect the efficiency of the equipment for any scheme. So, a collaborative model considering both the area stability and production capacity was established by combining the distance between the centers of the five ore blocks as an index. Differences in stability, deformation, and plastic zone size between the schemes are compared. The calculation results show that a mining scheme with a convex stepped shape produces the best results. These results provide a general method for entropy‐based mining sequence optimization and an optimal solution for the Tiaoshuihe phosphate mine.

Plastic Deformation Zone Size during Indenter Scratch Tests of Materials

The plastic deformation zone sizes in various metallic materials (steel, copper, armco-iron) are studied during tests by scratching with a tetrahedral Vickers pyramid under the scratch formation conditions at a constant depth. The ratio of the plastic deformation zone depth under a scratch to the scratch depth is found to weakly depend on the scratch depth and to be 6.3–8.5 for the materials under study. Based on these results, we concluded that, when the mechanical properties of a metallic material are determined by scratching, the ratio of the material thickness to the scratch depth should be at least 8.5.

Indentation and deformation behavior of FeCo-based bulk metallic glass alloys

FeCo-based bulk metallic glass with the compositions (Fe0.5Co0.5)69−xNb6B25+x (x=0, 2, 4) were cast using electric arc melting and suction casting technique. The samples were tested and analyzed in as-cast, sub-Tg annealed and partially crystalline conditions. Vicker’s microhardness was found to increase after annealing and partial crystallization. For high boron content hardness values approaching 1400 HV were obtained in partially crystalline samples. A compressive strength value of 4776MPa was calculated using hardness data. Sub-Tg annealing resulted in a decrease in the size of deformation zone formed underneath the hardness indenter after indentation. The bulk metallic glass alloys were embrittled by the partial crystallization treatment. It resulted in the formation of corner cracks during indentation. The size of the deformation zone increased with an increase in load. Semicircular and radial type of shear bands were observed as in the deformation zone with a higher number of radial shear bands observed in the annealed samples compared to as-cast samples. A comparison is made between the size of the deformation zone obtained experimentally and that predicted by the available models.

Effect of Surface Hardening Technique and Case Depth on Rolling Contact Fatigue Behavior of Alloy Steels

Surface hardening techniques are widely used to improve the rolling contact fatigue (RCF) resistance of materials. This study investigated the RCF resistance of hardened, ground steel rods made from three different aircraft-quality alloy steels (AISI 8620, 9310, and 4140) and hardened using different techniques (atmosphere carburizing, vacuum carburizing, and induction hardening) at different case depths. The RCF life of the rods was determined using a three ball-on-rod rolling contact fatigue test machine. After testing, the microstructures of the rods were examined using metallographic techniques. The stress distributions and plastic deformation zones for the specimens under RCF were calculated using an elastoplastic model for plastically graded materials. Relationships between surface hardness, case depth, and RCF life were investigated. The longest lives were observed for the vacuum-carburized AISI 9310 specimens, and the shortest lives were observed for the induction-hardened AISI 4140 specimens. It is concluded that the most important factors in determining the RCF lives of high-cleanliness surface-hardened alloy steels are (1) the hardness in the region of highest octahedral shear stress (in this case, ∼0.13 mm beneath the surface) and (2) the depth of high hardness (>613 HV), which determines the plastic deformation zone size.

Development and applications of forming-condition-based formability diagram for split concerns in stamping

This paper introduces an advanced, forming-condition-based formability diagram for accurately assessing the formability of complex stampings. The forming-condition-based formability diagram consists of a formability index that rationally define two curves (marginal line and safe line) and two zones (marginal zone and safe zone). The formability index measures deformation severity, tracks deformation history and predicts deformation trend. The safety factor, defined as the width of the marginal zone by means of the formability index, takes into account the forming conditions including deformation zone size, forming mode, bending process model, deformation history, metal flow pattern and post-necking deformation capacity of sheet metal. It is demonstrated that, rather than the traditional formability limit diagram, this formability diagram can more accurately quantify the formability status and can be used to determine the metal flow adjustment ranges for solving split problems. Its application to an automotive body side outer panel shows that it is a robust tool for formability engineering and troubleshooting through using numerical simulations and/or circle grid analysis.

Crystal Plasticity Finite Element Simulations of Polycrystalline Aluminium Alloy under Cyclic Loading

A three-dimensional crystal plasticity (CP) finite element model is developed to reproduce the grain level stress concentration and deformation of polycrystalline aluminium alloy 7075 (AA7075) during fatigue experiments. The grains contained in the model possess the same size and crystallographic orientations obtained from electron back-scatter diffraction experiments. A modified CP constitutive model, which considers the backstress evolution, is employed to describe the mechanical behaviour of AA7075 under cyclic loading. A round-notched specimen from a fatigue test is simulated using the proposed CP model. Convergence studies in terms of mesh density and plastic deformation zone size are carried out to determine the appropriate conditions for the simulation. The simulation results are compared with those obtained using the elasto-plastic model and the CP model without grain morphology. The comparison indicates that with the embedded grain morphology, the proposed model can capture very well the local response induced by the microstructure features, which is vital to the accurate fatigue life prediction of aluminium alloys.

On the subsurface deformation of two different Fe-based bulk metallic glasses indented by Vickers micro hardness

Bonded interface technique was employed to examine the nature of subsurface deformation during Vickers micro indentation in two iron-base bulk metallic glasses, (Fe0.9Ni0.1)77Mo5P9C7.5B1.5 (BMG-1) and Fe40Co8Cr15Mo13Y2C16B6 (BMG-2). Quantitative information such as the subsurface deformation zone size was recorded for indentation loads ranging from 200 to 5000 gr. The results showed that the BMG-2 specimens had an average hardness value higher than those observed in the BMG-1 specimens. The trends of the hardness vs. indentation load in the BMG-1 specimens were found to be related to the pressure sensitive index, while in the BMG-2 specimens, the cracking events and deformation-induced creation of free volume were responsible for the hardness tendency change. Observations of the deformation zones indicated that they deformed noticeably through two types of semi-circular and radial shear bands and the density of the radial shear bands was much more in the annealed specimens compared to the as-cast specimens. The relaxed and partially crystallized BMG-2 specimens exhibited cracking, ripple-like pattern as well as cracking and fragmentation, respectively. A simplified R = CP0.5 model was used to analyze the shear band zone size in the subsurface and specimens brittleness.

The microstructure and fracture performance of styrene–butadiene–methylmethacrylate block copolymer-modified epoxy polymers

The microstructure and fracture performance of an anhydride-cured epoxy polymer modified with two poly(styrene)-b-1,4-poly(butadiene)-b-poly(methyl methacrylate) (SBM) block copolymers were investigated in bulk form, and when used as the matrix material in carbon fibre reinforced composites. The ‘E21’ SBM block copolymer has a higher butadiene content and molecular weight than the ‘E41’. A network of aggregated spherical micelles was observed for the E21 SBM modified epoxy, which became increasingly interconnected as the SBM content was increased. A steady increase in the fracture energy was measured with increasing E21 content, from 96 to 511 J/m2 for 15 wt% of E21. Well-dispersed ‘raspberry’-like SBM particles, with a sphere-on-sphere morphology of a poly(styrene) core covered with poly(butadiene) particles, in an epoxy matrix were obtained for loadings up to 7.5 wt% of E41 SBM. This changed to a partially phase-inverted structure at higher E41 contents, accompanied by a significant jump in the measured fracture energy to 1032 J/m2 at 15 wt% of E41. The glass transition temperatures remained unchanged with the addition of SBM, indicating a complete phase separation. Electron microscopy and cross polarised transmission optical microscopy revealed localised shear band yielding, debonding and void growth as the main toughening mechanisms. Significant improvements in fracture energy were not observed in the fibre composites, indicating poor toughness transfer from the bulk to the composite. The fibre bridging observed for the unmodified epoxy matrix was reduced due to better fibre–matrix adhesion. The size of the crack tip deformation zone in the composites was restricted by the fibres, hence reducing the measured fracture energy compared to the bulk for the toughest matrix materials.

Experimental and Theoretical Investigation of Size Effects on the Ductile/Brittle Fracture Toughness of a Pressure Steel

Detailed un-standard experiments of fracture toughness in which SENB specimens of five different thicknesses were included, were carried out to investigate the size effect on the ductile and brittle fracture. It is found that the fracture toughness on the upper shelf increases with the size of the specimens, which have the similar geometry and then decreases gradually to the plane strain fracture toughness. The ductile fracture toughness increases with the size in the range of 4—16 mm for the increment of the plastic deformation zone size and plastic fracture strain under general yielding conditions, and then drops down from 16—22 mm for the increase of the high-stress triaxiality zone and the plastic deformation zone size not changing much which is less than the residual ligament width. While the fracture toughness of the lower shelf increases with the thickness in the range of 4—8 mm for the plastic deformation zone size increasing under small-scale yielding conditions, and then drops down from 8 to 22 mm for the increase of the high out-of-plane constraint. Theoretical analysis with the primary definition of the fracture toughness J integral, the constraint level and the plastic deformation volume was performed to investigate the different size effects for different temperatures. Finite Element Analysis simulations with continuum damage model to get the distribution and variety of the stress triaxiality as an important factor of fracture strain and fracture toughness.

Experimental Evaluation of the Size Effect on the Ductile and Brittle Fracture Toughness of a Steel Pressure Vessel

Experiments of fracture toughness with non-standard SENB specimens of five different thicknesses were performed to investigate the size effect on the ductile and brittle fracture for different temperatures. From the experimental results it is found that size effects both brittle and ductile fracture with the same trend but for different mechanical reasons. The ductile fracture toughness increases firstly with increased plastic deformation zone size and plastic fracture strain under general yielding conditions, and then drops down due to the plastic deformation zone size not changing much which is less than the residual ligament width and the increase of the proportion of the high stress triaxiality zone to the whole specimen. The fracture toughness of the lower shelf increases with increasing thickness of the plastic deformation zone size under small scale yielding conditions, and then drops down due to the increase of the high out-of-plane constraint.

Size effects on the ductile/brittle fracture properties of the pressure vessel steel 20 g

Detailed un-standard experiments of fracture toughness in which SENB specimens of five different thicknesses were included were carried out to investigate the size effect on the ductile and brittle fracture. It is found that the ductile fracture toughness parameter-the critical strain energy release rate increases with the size of the specimens which have the similar geometry shape and then decreases gradually to the plane strain fracture toughness. On the upper shelf the critical strain energy release rate increases with the size in the range of 4–16 mm for the increment of the plastic deformation zone size and plastic fracture strain under general yielding conditions, and then drops down from 16 mm to 22 mm for the plastic deformation zone size not changing much which is less than the residual ligament width and the increase of the proportional of the high stress triaxiality zone to the whole specimen. While on the lower shelf the critical strain energy release rate increases with the thickness in the range of 4–8 mm for the plastic deformation zone size increasing under small scale yielding conditions, and then drops down from 8 mm to 22 mm for the increase of the high out-of-plane constraint. Theoretical analysis with the primary definition of the strain energy release rate, the constraint level and the plastic deformation volume was performed to investigate the different size effects for different temperatures. FEA simulations with continuum damage model of GTN models to get the results of the stress triaxiality as an important factor of fracture toughness increasing with the reduction of the thickness.

Finite element analysis of the effect of back pressure during equal channel angular pressing

There is an increasing interest in applying back pressure during equal channel angular pressing (ECAP) to improve the process for better control of microstructure and property. The effect of increasing back pressure on deformation characteristics during ECAP such as the plastic deformation zone (PDZ) size and strain rate distribution in the PDZ, size of the corner gap and strain distribution on the longitudinal section were analysed by finite element analysis for both the quasi-perfect plastic and strain hardening materials. This investigation revealed that the back pressure influence very differently the PDZ of the quasi-perfect plastic and strain hardening materials. Many beneficial effects of back pressure were observed in the strain hardening material, with reduced PDZ size, dramatically reduced corner gap, and more uniform strain distribution. For the quasi-perfect plastic material, however, the application of increasing back pressure leads to broadening of PDZ and a decrease in strain rate homogeneity.

A critical examination of the relationship between plastic deformation zone size and Young's modulus to hardness ratio in indentation testing

Existing indentation models (both analytical models and numerical analysis) show a linear relationship between δr/δm and H/Er, where δr and δm are the residual and maximum indentation depth, and Er and H are the reduced Young's modulus and hardness of the test material. Based on the analysis of Oliver and Pharr, a new relationship between δr/δm and H/Er has been derived in a different way without any additional assumptions, which is nonlinear, and this has been verified by finite element analysis for a range of bulk materials. Furthermore, this new relationship for residual depth is used to derive an analytical relationship for the radius of the plastic deformation zone Rp in terms of the residual depth, Young’s modulus, and hardness, which has also been verified by finite element simulations for elastic perfectly plastic materials with different work hardening behavior. The analytical model and finite element simulation confirms that the conventional relationship used to determine Rp developed by Lawn et al. overestimates the plastic deformation, especially for those materials with high E/H ratio. The model and finite element analysis demonstrate that Rp scales with δr, which is sensible given the self-similarity of the indentations at different scales, and that the ratio of Rp/δr is nearly constant for materials with different E/H, which contradicts the conventional view.

Deformation morphology underneath the Vickers indent in a Zr-based bulk metallic glass

Hardness and plastic deformation during Vickers indentation in as-cast, annealed, and fully crystallized Zr 57Cu 27Al 11Ni 5 bulk metallic glass was examined. Subsurface deformation morphology under the indenter tip was studied at various loads and for different annealing time. Appreciable plastic deformation, through shear banding, occurs in the as-cast and annealed alloys. Two different types of shear bands are observed. Their occurrence depends upon the amount of annealing and hence on the extent of crystallization. The fully crystallized alloy exhibits extensive cracking. Trends in the deformation zone size with load are consistent with the expanding cavity model, while the shear band morphology, particularly for the as-cast sample, attests the qualitative applicability of the slip line field theory.

Deformation morphology underneath the Vickers indent in a Zr-based bulk metallic glass

Hardness and plastic deformation during Vickers indentation in as-cast, annealed, and fully crystallized Zr 57 Cu 27 Al 11 Ni 5 bulk metallic glass was examined. Subsurface deformation morphology under the indenter tip was studied at various loads and for different annealing time. Appreciable plastic deformation, through shear banding, occurs in the as-cast and annealed alloys. Two different types of shear bands are observed. Their occurrence depends upon the amount of annealing and hence on the extent of crystallization. The fully crystallized alloy exhibits extensive cracking. Trends in the deformation zone size with load are consistent with the expanding cavity model, while the shear band morphology, particularly for the as-cast sample, attests the qualitative applicability of the slip line field theory.

Subsurface deformation during Vickers indentation of bulk metallic glasses

Bonded interface technique was employed to examine the nature of subsurface deformation during Vickers indentation in two kinds of bulk metallic glasses (BMGs), $Pd_{42.1}Ni_{39.77}P_{18.13}$, and $Zr_{56.69}Cu_{26.96}Al_{10.95}Ni_{5.4.}$ Quantitative information such as the shear band spacing, pile-up length, subsurface deformation zone size etc. was recorded for indentation loads ranging from 50 to 5000 g. Experimental results show that both the BMGs have an average hardness value of $\sim$550 VHN with slightly higher hardness at low loads. Observations of deformation zones indicate that they deform appreciably through the shear band mechanism. For both bulk indentation, as well as the interface indentation, the normalized size of the deformation zone was found to be independent of the applied load. Two types of shear bands, radial, and semi-circular in nature, have been observed. These results are compared with similar studies made on ductile metals and silicate glasses.