Prediction Of Yield Strength Research Articles

Electronic structure & yield strength prediction for dislocation–Mo complex in the γ phase of nickel-based superalloys**Project supported by Beijing Municipality Science & Technology Commission, China (Grant No. D161100002416001).

Molybenum’s effects when added in the γ phase of nickel-based superalloys were studied using the lattice Green’s function multiscale method. The electronic structure of the dislocation–Mo complex was analyzed and hybridization was found to contribute to the strengthening. Moreover, by combining the interaction energies calculated from two scales, the yield stress was theoretically predicted at 0 K and finite temperature.

A modified Taylor model for predicting yield strength anisotropy in age hardenable aluminium alloys

Coherent precipitates have long been known to alter the anisotropy in mechanical properties of rolled products with respect to rolling direction, which is manifested in terms of yield strength anisotropy (YSA) of age hardenable wrought aluminium alloys. The effect of anisotropy of matrix due to texture and of precipitate due to its morphology has been captured previously using elastic and plastic inclusion approaches with limited success. In the present investigation, yield strength of polycrystalline sheet specimen of Al-Mg-Si alloy in different ageing conditions was calculated by considering solid solution, grain boundary and shearable precipitate strengthening. Effect of coherent directional precipitates on yield strength anisotropy was analyzed using both elastic as well as plastic inclusion models. Additional elastic or plastic work required to deform the precipitates is taken into account along with work done in deforming the matrix to predict YSA. The concept of effective Taylor factor that accounts for anisotropic contribution from precipitates and crystallographic texture of matrix is proposed and incorporated in the existing strengthening models to predict YSA in aged samples. It is observed that modified plastic inclusion model that incorporates anisotropy in flow stress of precipitates is able to capture the experimental YSA in differently aged samples. Universal nature of modified plastic inclusion model is demonstrated by extending the concept to Al-Zn-Mg-Cu alloy.

Predicting tensile properties of Ti-6Al-4V produced via directed energy deposition

Advanced manufacturing approaches, including additive manufacturing (i.e., “3D printing”) of metallic structures requires a change to qualification strategies. One approach, informed qualification, integrates modeling strategies to make predictions of material characteristics, including the prediction of tensile properties for given chemistries and microstructures. In this work, constitutive equations are developed and presented that can predict the yield strength of additively manufactured Ti-6Al-4V subjected to one of three different heat-treatments: a stress relief anneal in the α+β phase field; a hot isostatic press treatment in the α+β phase field; and a β-anneal. The equations are nominally identical, though different strengthening mechanisms are active according to subtle microstructural differences. To achieve an equation that can predict the yield strength of the material, it is also necessary to include an assessment of dramatic reduction in the tensile strength due to texture (i.e., a “knock-down” effect). This has been experimentally measured, and included in this paper. The resulting predictions of yield strength are generally within 5% of their experimentally measured values.

Reduced-order structure-property linkages for polycrystalline microstructures based on 2-point statistics

Computationally efficient structure-property (S-P) linkages (i.e., reduced order models) are a necessary key ingredient in accelerating the rate of development and deployment of structural materials. This need represents a major challenge for polycrystalline materials, which exhibit rich heterogeneous microstructure at multiple structure/length scales, and exhibit a wide range of properties. In this study, a novel framework is described for extracting S-P linkages in polycrystalline microstructures that are obtained using 2-point spatial correlations (also called 2-point statistics) to quantify the material's microstructure, and principal component analysis (PCA) to represent this information in a reduced dimensional space. Additionally, it is demonstrated that the use of generalized spherical harmonics (GSH) as a Fourier basis for functions defined on the orientation space leads to a compact and computationally efficient representation of the desired S-P linkages. In this study, these novel protocols are developed and demonstrated for elastic stiffness and yield strength predictions for α− Ti microstructures using a dataset produced through microscale finite element simulations.

Design and development of force and torque measurement setup for real time monitoring of friction stir welding process

Abstract The aim of the present research work is two folded. First, it is intended to describe the development of a low cost force measurement setup for friction stir welding (FSW) process and second, is to demonstrate the potential of force signals combined with artificial intelligence to accurately predict ultimate tensile strength (UTS) and yield strength of the joints. In FSW process, simultaneous rotation, and translation of the tool associated with severe plastic deformation of material around the tool pin brings challenges in measurement of torque and forces experienced during welding. An attempt has been made to design and develop a strain gauge based setup for the measurement of two dimensional forces and torque during FSW process. The force signals acquired using the developed setup is then utilized to develop support vector regression based data driven models for prediction of UTS and yield strength of the welded samples. For monitoring the FSW process a new statistical indicator derived from force signals is presented. The proposed indicator brings appreciable correlation with the UTS of the joints. The prediction performances of the developed models imply that the presented approach can be effectively put forward for real time monitoring of the process.

Prediction of yield strength of MWCNT/PP nanocomposite considering the interphase and agglomeration

The yield strength of multi-walled carbon nanotube/polypropylene (MWCNT/PP) nanocomposite of 2wt% is predicted using a two-scale continuum model. In the nano-scale, FE models of representative unit cells (RUCs) consisting of MWCNT agglomerates, the surrounding PP matrix and the interphase between them are developed using TexGen software and ANSYS Workbench. The geometries of the agglomerates were determined from processing and analysis of scanning electron microscopy images of the MWCNT/PP material. The characteristics of the interphase were determined from atomic force microscopy images and nanoindentation tests conducted on MWCNT/PP specimens. The FE models of the RUCs were solved using the LS-DYNA explicit FE code. The non-linear behavior of the PP material was modeled using an elastic-plastic material model for which input data were obtained from uniaxial tension tests. The simulated behavior of the RUCs was assigned to the elements of the FE model of a tension specimen which was used to predict the yield strength of the MWCNT/PP material. The model predictions show a high sensitivity of yield strength with the characteristics of the MWCNT/PP interphase.

Quantifying the effect of microstructure variability on the yield strength predictions of Ni-base superalloys

Physics-based models for predicting the mechanical behavior of Ni-based superalloys as a function of microstructure features require the use of microstructure data for calibration and verification. Accurate representation of the heterogeneity of microstructure features requires accurate selection of the representative microstructure data size (i.e. image size). Thus, this work is carried out to address the influence of microstructure data size on the accuracy of a discrete dislocation dynamic model in predicting the critical resolved share stress (CRSS) of IN100. Microstructure features from backscattered electron images were extracted using image processing techniques. Single point statistics (e.g. area fraction, precipitate size, and distance between γ` particles) and higher order statistics using two-point correlations were calculated from segmented 2-D images. Modified Bhattacharyya Coefficient analysis techniques were employed to calculate three-dimensional particle size distributions. Results indicate a significant influence of the microstructure data size on the calculated CRSS.

Comparative Assessment of Strength Models for AA6063 Alloy

This report presents a comparative assessment of the suitability of two existing physical models for predicting yield strength of artificially aged AA6063 Al-alloy. One model is based on the modified Orowan mechanism of dislocation by-pass for non-shearable rod shaped precipitates rejuvenated by Zhu and Stark, and the other model is based on classical dislocation-particle interaction that incorporates both cutting and by-pass mechanisms for spherical shaped precipitates developed by Deschamps and Brechet. Using these models, simulation of yield strength values have been performed considering nucleation-growth as well as nucleation-growth-coarsening of precipitates during the entire period of ageing. Comparison of experimental and simulated results reveals that the model by Deschamps and Brechet predicts yield strength more accurately when nucleation-growth-coarsening of precipitates are incorporated.

Not only stiffness, but also yield strength of the trabecular structure determined by non-linear µFE is best predicted by bone volume fraction and fabric tensor

The micro-architecture of cancellous bone is considered a major determinant of the fracture risk. Yet, if morphometry tells about alterations of the trabecular network, its elastic behaviour is best described by bone volume fraction (BV/TV) and the fabric tensor, which gives the anisotropy of the trabecular structure. This remains to be proven for yield strength, the onset of bone failure. The microstructure of 126 samples extracted from femoral heads of two female subjects was evaluated on micro-computed tomography scans via 25 structural indices. Parameters such as plate and rod decomposition via ITS and textural analyses by ISV, similar to the trabecular bone score, were also examined. The degree of collinearity between indices was assessed. The indices considered sufficiently independent were included in multi-linear regression models predicting stiffness or yield strength measured via nonlinear micro finite element analyses. The models' accuracy was checked and the contributions of all explanatory variables to the prediction were compared. Our results show that BV/TV alone explained most of the predicted yield strength (76%) and stiffness (89%). BV/TV together with the fabric tensor explained more than 98% of both measures! The fabric tensor also had a larger impact on yield strength (23%) than on the stiffness predictions (9%). On the other hand, the predictive value of the other independent factors (Tb.Th.SD, Tb.Sp.SD, rTb.Th, RR.Junc.D, ISV) was negligible (<1%). In conclusion, just as stiffness, yield strength of femoral trabecular bone is also best explained by BV/TV and trabecular anisotropy, the latter being even more relevant in its post-elastic behaviour.

Tensile properties and temperature-dependent yield strength prediction of GH4033 wrought superalloy

The tensile properties of superalloy GH4033 have been evaluated at temperatures ranging from room temperature to 1000°C. Fracture surfaces and precipitation were observed using a field-emission scanning electron microscope (FE-SEM). The alloy mainly consisted of γ’ precipitate particles homogeneously dispersed in the γ matrix interior. The effects of dynamic strain aging and precipitation on the strength were verified. A temperature-dependent yield strength model was developed to describe the temperature and precipitation effects on the alloy's yield behaviour. The model is able to consider the effect of precipitation strengthening on the yield strength. The yield behaviour of the precipitation-strengthened superalloy was demonstrated to be adequately predictable over a wide range of temperatures. Note that this model reflects the quantitative relationship between the yield strength of the precipitation-strengthened superalloy and the temperature, the elastic modulus, the specific heat capacity at constant pressure, Poisson's ratio, the precipitate particle size and the volume fraction of the particles.

Weld quality prediction in friction stir welding using wavelet analysis

The paper aims to present the application of wavelet packet transformation for feature extraction from the signals acquired during friction stir welding of aluminum alloy. One of the challenges encountered while implementing wavelet packet transformation is the selection of an appropriate mother wavelet function. In this study, a new method is proposed for the selection of an appropriate mother wavelet function based on the ratio of energy of the signal to the entropy of the decomposed wavelet packets. Main spindle motor and feed motor current signals are acquired during 65 welding experiments designed through full factorial method by varying three process parameters in four levels. Features obtained from wavelet packet transformation along with process parameters are fed to two artificial neural network models: multi-layer feed-forward neural network model trained with back propagation algorithm and radial basis function neural network model for the prediction of ultimate tensile strength and yield strength of the welds. The prediction performance of the former model is found to be superior to the later model for both ultimate tensile strength and yield strength.

Mechanical Properties and Strengthening Mechanisms of Al-15 Pct B4C Composites with Sc and Zr at Elevated Temperatures

The mechanical properties at ambient and elevated temperatures of two Al-15 vol pct B4C composites, S40 with 0.4 wt pct Sc and SZ40 with 0.4 wt pct Sc and 0.24 wt pct Zr, are investigated during long-term thermal annealing. The presence of large B4C particles in the microscale has a moderate but stable strengthening effect on Al-B4C composites at ambient and elevated temperatures, while the precipitation of nanoscale Al3Sc and Al3(Sc, Zr) in the composite matrix provides a predominate contribution to the composite strength, which is varied by tested temperatures. The Al3Sc precipitates in S40 remain coarsening resistant at 523 K (250 °C), whereas the Al3(Sc, Zr) precipitates in SZ40 are thermally stable at 573 K (300 °C) over 2000 hours of annealing. At higher annealing temperatures (573 K (300 °C) for S40 and 623 K (350 °C) for SZ40), both Al3Sc and Al3(Sc, Zr) precipitates become coarsening with prolonged annealing time. The yield strength of S40 and SZ40 at ambient temperature decreases with the increasing precipitate size, which can be explained by the classical precipitate shearing and Orowan bypass mechanisms. At elevated temperatures [523 K to 623 K (250 °C to 350 °C)], considerably lower yield stresses are observed compared to those at ambient temperature, which invokes a dislocation climb mechanism. The predicted yield strengths at elevated temperatures by the combination of dislocation climb and Orowan models are in good agreement with the experimental data.

A Multiple-Mechanism-Based Model for Prediction of Yield Strength in Bicrystals

Different mechanisms such as glide of lattice dislocation and grain boundary mediated processes may be active during the plastic deformation of polycrystals with small grain size. A continuum model for polycrystal plasticity has been developed to capture such a feature. Specifically, the strain gradient effect due to dislocation pile-up, dislocation emission/absorption at surface and grain boundary sliding have been taken into account from the perspective of energy storage. As an application of the model, a bicrystal under plane constrained shear has been considered. The dependence of yield strength on the thickness of the bicrystal has been investigated. It has been demonstrated the present model predicts the yield strength of the bicrystal first increases and then decrease with decrease in the thickness, which is similar to the inverse Hall–Petch behavior but with a different scaling. Such behavior is attributed to the transition in different dominant deformation mechanisms at different values of the thickness.

Simulating Size and Volume Fraction-Dependent Strength and Ductility of Nanotwinned Composite Copper

This work presents a micromechanical model to investigate mechanical properties of nanotwinned dual-phase copper, consisting of the coarse grained phase and the nanotwinned phase. Both strengthening mechanisms of nanotwinning and the contributions of nanovoids/microcracks have been taken into account in simulations. With the aid of modified mean-field approach, the stress–strain relationship is derived by combining the constitutive relations of the coarse grained phase and the nanotwinned phase. Numerical results show that the proposed model enables us to describe the mechanical properties of the nanotwinned composite copper, including both yield strength and ductility. The calculations based on the proposed model agree well with the results from finite element method (FEM). The predicted yield strength and ductility are sensitive to the twin spacing, grain size, as well as the volume fractions of phases in this composite copper. These results will benefit the optimization of both strength and ductility by controlling constituent fractions and the size of the microstructures in metallic materials.

A multiscale gradient-dependent plasticity model for size effects

The mechanical behaviour of polycrystalline material is closely correlated to grain size. In this study, we investigate the size-dependent phenomenon in multi-phase steels using a continuum dislocation dynamic model coupled with viscoplastic self-consistent model. We developed a dislocation-based strain gradient plasticity model and a stress gradient plasticity model, as well as a combined model, resulting in a theory that can predict size effect over a wide range of length scales. Results show that strain gradient plasticity and stress gradient plasticity are complementary rather than competing theories. The stress gradient model is dominant at the initial strain stage, and is much more effective for predicting yield strength than the strain gradient model. For larger deformations, the strain gradient model is dominant and more effective for predicting size-dependent hardening. The numerical results are compared with experimental data and it is found that they have the same trend for the yield stress. Furthermore, the effect of dislocation density at different strain stages is investigated, and the findings show that the Hall–Petch relation holds for the initial strain stage and breaks down for higher strain levels. Finally, a power law to describe the size effect and the transition zone between the strain gradient and stress gradient dominated regions is developed.

Predicting yield strengths of Al-Zn-Mg-Cu-(Zr) aluminium alloys based on alloy composition or hardness

A linear single variable model for describing precipitation heat treated Al-Zn-Mg-Cu aluminium alloy hardness and yield strength based on precipitate compositions was proposed. A concept composition model was developed based on the major alloying elements and the strengthening precipitate compositions, for the precipitation heat treatment condition. A Refined composition model was subsequently developed to account for the effect of minor alloying (Mn) and impurity elements (Fe, Si). Macro segregation of alloying elements had a significant effect on the results of the Refined composition model. Mechanical properties varied according to a simple linear relationship with the atomic fraction of the strengthening precipitate. The T6 and T73 hardness, and T6 yield strength were algebraically expressed, with linear relationships. The model describes existing yield strength data for Al-Zn-Mg-Cu aluminium alloys. The Refined composition model was also valid for predicting yield strengths of Al-Zn-Mg-Cu-Zr aluminium alloys in the T6 condition.

Developing a phenomenological equation to predict yield strength from composition and microstructure in β processed Ti-6Al-4V

A constituent-based phenomenological equation to predict yield strength values from quantified measurements of the microstructure and composition of β processed Ti-6Al-4V alloy was developed via the integration of artificial neural networks and genetic algorithms. It is shown that the solid solution strengthening contributes the most to the yield strength (~80% of the value), while the intrinsic yield strength of the two phases and microstructure have lower effects (~10% for both terms). Similarities and differences between the proposed equation and the previously established phenomenological equation for the yield strength prediction of the α+β processed Ti-6Al-4V alloys are discussed. While the two equations are very similar in terms of the intrinsic yield strength of the two constituent phases, the solid solution strengthening terms and the ‘Hall-Petch’-like effect from the alpha lath, there is a pronounced difference in the role of the basketweave factor in strengthening. Finally, Monte Carlo simulations were applied to the proposed phenomenological equation to determine the effect of measurement uncertainties on the estimated yield strength values.

Effect of surface energy upon size-dependent yield strength of single-crystalline hollow micro- and nanopillars

The physical nature of the size-dependent yield strength of micro- and nanopillars is still an open issue, where the surface energy may be one factor that influences the size effect of these pillars, especially for hollow pillars. In this study, the influence of the surface energy and surface elasticity upon the size-dependent yield strength of single-crystalline hollow micro- and nanopillars is considered quantitatively. An analytical expression of the size-dependent yield strength is established that considers the surface energy and the inner defects by the principle of minimum potential energy. The predicted yield strength of our model as a function of the pillar size is more precise than that of the well-known single arm source model when comparing the predictions with the experimental results of pillars made of Al or Ni. According to the surface elasticity, the surface energy can be determined by the thickness of the hollow pillars, the surface modulus and the surface strain, where the latter two are related to the external damages.

Tailoring the mechanical properties of steel sheets using FeC films and diffusion annealing

In this work amorphous FeC films were deposited on thin sheets of interstitial free steel using physical vapor deposition. Annealing treatments were then carried out to diffuse C from the coating into the substrate at temperatures lower than those traditionally used in carburizing treatments. The yield stress was shown to significantly increase with annealing temperature from ~120MPa at 25°C up to a maximum of 300MPa at 630°C without any significant loss of ductility. At 710°C, a decrease in yield strength was related to the coarsening of carbides inside the IF steel (confirmed by atom probe tomography), and the associated reduction in the matrix solid solution carbon concentration (confirmed by thermoelectric power measurements). The through-thickness carbon diffusion profile was predicted using Fick's law and validated by Knoop hardness measurements. Yield strength predictions were accurate if the crystallization of the FeC film was taken into account as it controls the amount of carbon available to be diffused in the interstitial free steel substrate.

Yield and ultimate strengths determination of a blind bolted endplate connection to square hollow section column

This paper evaluates the yield and ultimate strengths of a blind bolted endplate to square tubular column connection in joint tensile region. It outlines a research work of eleven connection tests with focus on the strengths of the connection components under tensile loads. The influences of the bolt gauge width, slenderness of tubular columns and bolt size details on the strengths of the connections in three failure modes are reported. Based on the experimental test results, yield strength determination methods are examined and discussed on the basis of deformations of the tube connecting face and the overall connection. Finite element models explicitly allowing for the configuration details of the Hollo-Bolt are then presented and compared with the test results. Subsequently, an analytical model is proposed for the prediction of yield strength with due consideration given to the plastification of SHS column and combined action of the blind bolt related to three failure modes. Based on an augmented consideration of membrane effect and circumferential locking action of the Hollo-Bolt, the analytical model is also extended for the prediction of ultimate strength. Additionally, two geometric parameters in characterizing the failure modes of the connection are discussed from a numerical parametric study. The analytical results presented in this paper provide some essential information for the strength design recommendations of such a blind bolted endplate connection to square tubular column.