Microscopic Stress Distribution Research Articles

Uniaxial tensile‐induced deformation of spherulite: combining experimental and simulation methods

AbstractA combination of experimental and simulation methods is adopted to study the relationship between micro‐stress and micro‐strain of a single spherulite upon uniaxial tensile deformation. To verify the simulation results and establish a suitable spherulite model, large‐sized isotactic polypropylene spherulite is first cultured with isothermal crystallization, whose structural deformation upon application of uniaxial tension is recorded using a polarizing optical microscope. A nanoindenter is used to measure the elastic modulus of the spherulite and amorphous region, preparing the property parameters for numerical simulation. Modeling and meshing of the single spherulite are conducted with the finite element software ABAQUS. The entire deformation of the spherulite is analyzed with fixed strain as the boundary condition, and the microscopic stress and strain distribution inside and outside of the spherulite is obtained. The higher micro‐stress region mainly locates at two poles in the equatorial direction, where might be the origin of craze. Generally, the simulation result is basically consistent with the experimental deformation process, which provides a new idea for the study of microscale structure and performance. © 2024 Society of Chemical Industry.

Water quenching cracking mechanism and prevention of steels

ABSTRACTQuenching is often an essential step in heat treatment of steels for enhancing strength. Water quenching which is low cost and free of pollution risk instead of oil quenching or polymer aqueous solution quenching which is high cost and has high pollution risk will be widely used in heat treatment enterprises. However, the problem of easy cracking of low alloy steels (especially medium carbon low alloy steels) quenched in water has long been a concern for many researchers. The finite element simulation (FES) is used to predict transient stress at cracking position during quenching of an AISI 4140 steel cylinder sample and found that the transient tangential tensile stress at cracking position was only 350 MPa which is smaller than half of the yield strength (775 MPa) of AISI 4140 steel. Such a low tensile stress causing quenching cracking is surprising. To ascertain the underline reasons, a phase-field finite element (PFFE) model is established to investigate the microscopic stress distribution produced by martensitic transformation. The results indicate that the microscopic stress at the junction of the lath martensitic variants in AISI 4140 steel exceeded 800 MPa, and thus such a high microscopic stress is considered as the origin of quenching cracking. By using two examples, our work further clarifies the basic principle of the water–air alternative timed quenching (ATQ) process invented by us as a process suitable for engineering applications with the ability to avoid water quenching cracking and ensure mechanical properties.

A three-scale layerwise multiscale analysis method for composite laminated plates

Based on Reddy’s layerwise theory (RLWT) and the O(1) homogenization method, a three-scale layerwise multiscale analysis method (LMAM) is proposed for composite laminated plates. This method takes periodicity in both in-plane and thickness directions into account. The RLWT is utilized to discretize the macroscopic model of a composite laminated plate, and three-dimensional (3D) finite elements are used to establish the mesoscopic and microscopic cell models composed of fibers and matrix. The numerical simulation of square plate with inclusions is conducted by the presented LMAM, the results of which are compared with direct numerical simulation (DNS) and O(1) homogenization approach to verify the LMAM. The LMAM is also used to calculate and analyze the macroscopic, mesoscopic and microscopic stress distributions of woven composite laminated plates.

Intelligent Testing and Analysis of Dissimilar Steel Welds for Industrial Throttle Flowmeter

The throttling flowmeter used in utility boilers has been used as a measuring instrument for a long time. However, its safety performance, such as welding, lacks enough attention. The manufacturing welds of the throttling flowmeter are welded with austenitic stainless steel and pearlitic heat-resistant steel. Cracks and other defects are generally found in the inspection and detection of the manufacturing welds of throttling flowmeters in service, which have serious potential accidents. To find out the relationship between weldingdissimilar steels and defects, the microhardness indentation method was used to measure the residual stress of welding. Combined with the self-developed calculation software of microscopic indentation residual stress distribution, we used the difference between the color of the indentation area and the surrounding area to quickly measure the indentation strain collected by the microscope using the computer image recognition algorithm, which greatly improved the accuracy and speed of the microscopic indentation residual stress test. The results show that the residual stress at the weld of dissimilar steel is relatively large, and the mechanical property test is generally unqualified. The microindentation residual stress analysis method based on computer image recognition is used to quickly, intuitively, and accurately reveal the direct relationship between the combination of dissimilar steel welding materials and the generation of cracks and other defects.

In Situ Nanostress Visualization Method to Reveal the Micromechanical Mechanism of Nanocomposites by Atomic Force Microscopy.

An in situ atomic force microscopy (AFM) nanomechanical technique was used to directly visualize the micromechanical behaviors of polymer nanocomposites during compressive strain. We obtained a stress distribution image of carbon black (CB)-filled rubber at the nanoscale for the first time, and we traced the microscopic deformation behaviors of CB particles. Through this experiment, we directly revealed the microscopic reinforcement mechanisms of rubber composites. We found that CB-filled rubbers exhibited heterogeneous local microscopic deformations, which were related to the dispersion of CB particles in rubber matrices. The local stress distributions of the rubber composites showed heterogeneity, and the stresses were concentrated in the regions near the CB particles during compression. The area of stress concentration gradually expanded with increasing strain and eventually formed a stress network structure. This stress network bore most of the macroscopic stress and was considered the key reinforcement mechanism of CB-filled rubber. The stress transfer process in the rubber matrix was visualized in real space for the first time. Based on the image data from the AFM experiments, we used finite-element method (FEM) simulations to reproduce the microscopic deformation process of CB-filled rubber. The stress distribution images simulated by FEM showed heterogeneity consistent with AFM. In this study, an in situ visualization of material deformation confirmed the predictions of microscopic deformation behavior from previous theories and models; it also provided new insights into the microscopic reinforcement mechanisms of CB-filled rubber composites based on microscopic stress distribution images.

PH-Net: Parallelepiped microstructure homogenization via 3D Convolutional Neural Networks

Microstructures are attracting academic and industrial interest because of the rapid development of additive manufacturing. The numerical homogenization method has been well studied for analyzing mechanical behaviors of microstructures; however, it is too time-consuming to be applied to online computing or applications requiring high-frequency calling, e.g., topology optimization. Data-driven homogenization methods are considered a more efficient choice but the microstructures are limited to cubic shapes, therefore are unsuitable for periodic microstructures with a more general shape, e.g., parallelepipeds. This paper introduces a fine-designed 3D convolutional neural network (CNN) for fast homogenization of parallelepiped microstructures, named PH-Net. Superior to existing data-driven methods, PH-Net predicts the local displacements of microstructures under specified macroscopic strains instead of direct homogeneous material, empowering us to present a label-free loss function based on minimal potential energy. For dataset construction, we introduce a shape-material transformation and voxel-material tensor to encode microstructure type, base material and boundary shape together as the input of PH-Net, such that it is CNN-friendly and enhances PH-Net on generalization in terms of microstructure type, base material, and boundary shape. PH-Net predicts homogenized properties hundreds of times faster than numerical homogenization and even supports online computing. Moreover, it does not require a labeled dataset and thus the training process is much faster than current deep learning methods. Because it can predict local displacement, PH-Net provides both homogeneous material properties and microscopic mechanical properties, e.g., strain and stress distribution, and yield strength. We also designed a set of physical experiments using 3D printed materials to verify the prediction accuracy of PH-Net.

Effect of distribution characters of ferrite/bainite on deformation compatibility in dual-phase pipeline steel: Experimental and numerical study

The morphology distribution of microstructure has an important influence on the match of the strength and plasticity of dual-phase pipeline steel. Bainite and PF dual-phase steels with layered and network morphology were obtained by combining the Thermomechanical Control Process (TMCP) and inter-critical isothermal heat treatment. A novel experimental-numerical methodology studied the effect of phase distribution characters on the deformability of PF and bainite dual-phase pipeline steel. The plastic damage features and microscopic strain and stress distribution in both network and layered microstructure were clarified. The obvious differences in the microstructure evolution for both samples were captured by a quasi-situ tensile test. The PF phase in the network morphology sample was believed the main deformation phase, but the deformation of the PF phase in the layered morphology sample was restrained. Two three-dimensional (3D) crystal plasticity finite element models (CPFEMs) were established based on the electron backscatter diffraction (EBSD) data. The simulation results indicated that the strain field in layered microstructure was more uniform than that in network microstructure, and the continuous internal stress relaxation (ISR) in the bainite phase led to plastic damage at low tensile strain level; The strain field in network microstructure mainly existed in the PF phase, the deformation of the PF phase can be fully utilized. When changing the tensile x-direction of the layered microstructure to the z-direction, the strain field showed an obvious anisotropy, and loading in the z-direction increased the risk of interlaminar crack formation. • Quasi-situ tensile test was used to study the deformation behavior • Strain/stress distribution characteristics were clarified using CPFEM method • Uniform strain distribution and ISR in layered microstructure decreased its plasticity • z-axis loading increased the risk of interlaminar crack for layered microstructure

Direct visualization of stretch-induced phase separation in methoxy silyl-terminated polypropylene oxide/epoxy resin-type polymer alloys via AFM nanomechanics: A toughening mechanism

Methoxy silyl-terminated polypropylene oxide (MS-PPO) has been widely used as an adhesive between different materials and has resulted in substantially improved elongation properties by alloying with epoxy resins (EPX). The fracture stress of MS-PPO/EPX polymer alloys can also be significantly increased by the further addition of silane coupling agents. However, the microscopic mechanisms underlying the toughening of such polymer alloys have not been clarified due to the lack of characterization of the microscopic mechanical properties. In this study, we characterized the nanoscale mechanical properties of MS-PPO/EPX polymer alloys using atomic force microscopy (AFM) nanomechanics. We found that silane coupling agents increased the compatibility of MS-PPO and EPX, leading to the nanoscale dispersion of EPX in MS-PPO, forming a MS-PPO-rich phase matrix. By tracing the microscopic stress distribution and deformation behavior of these materials using AFM nanomechanics, it was found that polymer alloys with different compositions exhibited different microscopic toughening mechanisms. Microscopic stretch-induced phase separation (SIPS) occurred in the MS-PPO-rich phase matrix, resulting in improved macroscopic tensile properties. The SIPS phenomenon is crucial for alloy toughening, providing new insights into the toughening mechanism of polymer alloys.

Stiffness and strength evaluation of lattice-based mechanical metamaterials by decoupled two-scale analysis

There is an emerging class of artificial materials, so-called mechanical metamaterials. By deliberately designing microscopic internal mechanisms, these materials exhibit exotic properties, which distinguish the mechanical metamaterials from natural materials. As additive manufacturing technology has been rapidly developed and its manufacturing quality has been improved, those conceptual artificial materials are ready to fabricate. This paper presents a decoupled two-scale analysis framework to efficiently evaluate the stiffness and strength characteristics of lattice-based mechanical metamaterials. Structural characteristics of lattice-based mechanical metamaterials are effectively captured by accommodating a computational homogenization method to lattice-based structures. In the computational homogenization procedure, a unit cell of the periodically distributed structure is modeled as representative finite elements. Equivalent stiffness properties of the unit cell are calculated based on the computational homogenization procedure. The equivalent structural properties are then used to perform macroscopic structural analysis of lattice-based structures in an effective manner. Similarly, a local/microscopic stress distribution within the periodic lattice unit cell is recovered by transforming macroscopic sectional loads, which are obtained from the macroscopic structural analysis, through a stress amplification matrix. The microscopic stress distribution obtained with the two-scale analysis can be used for strength evaluation. Subsequently, numerical results are validated by comparing them with experimental results providing actual behaviors of lattice-based mechanical metamaterials. This work presents the novel use of the multi-scale analysis scheme combining the computational homogenization method and the stress field transformation method enabling structural evaluations to design mechanical metamaterials with structural integrity. This study also demonstrates the feasibility and capability of the presented approach to effectively predict stiffness and strength characteristics of lattice-based structures.

Ph-Net: Parallelepiped Microstructure Homogenization Via 3d Convolutional Neural Networks

Microstructures are attracting academic and industrial interests with the rapid development of additive manufacturing. The numerical homogenization method has been well studied for analyzing mechanical behaviors of microstructures; however, it is too time-consuming to be applied to online computing or applications requiring high-frequency calling, e.g., topology optimization. Data-driven homogenization methods emerge as a more efficient choice but limit the microstructures into a cubic shape, which are infeasible to the periodic microstructures with a more general shape, e.g., parallelepiped. This paper introduces a fine-designed 3D convolutional neural network (CNN) for fast homogenization of parallel-shaped microstructures, named PH-Net. Superior to existing data-driven methods, PH-Net predicts the local displacements of microstructures under specified macroscope strains instead of direct homogeneous material, motivating us to present a label-free loss function based on minimal potential energy. For dataset construction, we introduce a shape-material transformation and voxel-material tensor to encode microstructure type,base material and boundary shape together as the input of PH-Net, such that it is CNN-friendly and enhances PH-Net on generalization in terms of microstructure type, base material, and boundary shape. PH-Net predicts homogenized properties with hundreds of acceleration compared to the numerical homogenization method and even supports online computing. Moreover, it does not require a labeled dataset and thus is much faster than current deep learning methods in training processing. Benefiting from predicting local displacement, PH-Net provides both homogeneous material properties and microscopic mechanical properties, e.g., strain and stress distribution, yield strength, etc. We design a group of physical experiments and verify the prediction accuracy of PH-Net.

Reinforcement Mechanism of Carbon Black-Filled Rubber Nanocomposite as Revealed by Atomic Force Microscopy Nanomechanics.

In this study, atomic force microscopy (AFM) nanomechanics were used to visualize the nanoscale stress distribution in carbon black (CB)-reinforced isoprene rubber (IR) vulcanizates at different elongations and quantitatively evaluate their volume fractions for the first time. The stress concentrations in the protofibrous structure (stress chains) that formed around the CB filler in CB-reinforced IR vulcanizates were directly observed at the nanoscale. The relationship between the local nanoscale stress distribution and macroscopic tensile properties was revealed based on the microscopic stress distribution and microscopic spatial structure. This study can help us gain insight into the microscopic reinforcement mechanism of carbon black-containing rubber composites.

A method for predicting subsurface fatigue life of rolling bearings based on macro–micro coupling model

The fatigue life of the bearing can be predicted effectively by combining the multifield coupling condition of the working process with the internal microstructure. In this paper, a bearing fluid lubrication model is established based on the computational fluid dynamics method, and the calculation result is coupled to the thermal-solid model by the grid mapping method. Through this method, a bearing thermal-fluid-solid multifield coupling dynamics model is established to obtain the evolution information of bearings. Simultaneously, the micro-characterization experiments of SKF6406 bearing (M50 bearing steel) were carried out by electron backscatter diffraction, scanning electron microscope and nano-indentation. The microstructure model of bearing containing micro-inclusions was established by the Voronoi method. On this basis, the microscopic stress distribution characteristics and the motion law of bearing microstructure under the multifield coupling action are solved. In the end, the fatigue life prediction method of rolling bearing was established.

Tunnel failure mechanism during loading and unloading processes through physical model testing and DEM simulation

Geo-materials may present varying mechanical properties under different stress paths, especially for tunnel excavation, which is typically characterized by the decreased radial stress and increased axial stress during the complex loading and unloading process. This study carried out a comparative analysis between the loading and unloading model testing, which was then combined with PFC2D simulation, aiming to reveal the fracture propagation pattern, microscopic stress and force chain distribution of the rock mass surrounding the tunnel. Comparisons of extents and development of tensile strain between loading and unloading testing results were made. The overall stability, the integrity of rock mass, and the failure pattern transition under loading and unloading processes were systematically examined. In addition, for the two unloading cases with different vertical stresses imposed, the failure patterns were both identified as the collapse of the V − shaped extruded sidewall, due to the coupling of the shear failure and the vertical tensile failure in the sidewall wedge.

A layerwise multiscale analysis method for composite laminated plates

In the two-dimensional shear deformation theories (SDT) of composite laminates, the three-dimensional plates or shells are transferred to a two-dimensional problem in the reference surface by introducing displacement fields and stress resultants along the thickness direction, the constitutive relationship is a resultant form. The multiscale analysis methods developed from SDT can not describe the periodicity along the thickness direction in composite laminated plates and shells, so it is almost impossible to accurately analyze the local stress fields surrounding the fibers based on the two scale analysis scheme. A two scale layerwise multiscale analysis method (LMAM) is established based on the Reddy’s layerwise theory (RLWT) and O(1) homogenization method for the composite laminated plates, considering the periodicity in in-plane and along the thickness direction simultaneously. The macroscopic problem of laminated plate is discretized by RLWT, while the unit cells consisted by fiber and matrix are modeling by three-dimensional finite elements. In numerical examples, the proposed LMAM is verify by using direction numerical simulation (DNS) and the O(1) homogenization method based on three-dimensional macroscopic finite elements. The unidirectional and woven composite plates are studied by the proposed LMAM; the macroscopic and microscopic stress distributions along the thickness are investigated.

{text {FE}}^r method with surrogate localization model for hyperelastic composite materials

This study presents a method for constructing a surrogate localization model for a periodic microstructure, or equivalently, a unit cell, to efficiently perform micro-macro coupled analyses of hyperelastic composite materials. The offline process in this approach is to make a response data matrix that stores the microscopic stress distributions in response to various patterns of macroscopic deformation gradients, which is followed by the proper orthogonal decomposition (POD) of the matrix to construct a reduced order model (ROM) of the microscopic analysis (localization) with properly extracted POD bases. Then, response surfaces of the POD coefficients are constructed so that the ROM can be continuous with respect to the input datum, namely, the macroscopic deformation gradient. The novel contributions of this study are the application of the L2 regularization to the interpolation approximations of the POD coefficients by use of radial basis functions (RBFs) to make the response surfaces continuous and the combined use of the cross-validation and the Bayesian optimization to search for the optimal set of parameters in both the RBFs and L2regularization formula. The resulting model can be an alternative to microscopic finite element (FE) analyses in the conventional {text {FE}}^2 method and realizes {text {FE}}^r with 1<r<<2 accordingly. Representative numerical examples of micro-macro coupled analysis with the {text {FE}}^r are presented to demonstrate the capability and promise of the surrogate localization model constructed with the proposed approach in comparison with the results with high-fidelity direct {text {FE}}^2.

Failure analysis of fiber-reinforced composites subjected to coupled thermo-mechanical loading

Structures made of fiber reinforced composites have captured extensive attentions in the scientific and engineering communities due to their excellent performance and applicability. When these structures are in service, they are likely exposed to variations of ambient temperature that may have an impact on their strength. To study this effect, a coupled thermo-mechanical model is required. This paper develops a microscopic mechanical model to investigate failure of composite structures subjected to a coupled thermo-mechanical condition. Stiffness degradations of composite laminates are first investigated. A comparison between experimental data and theoretical results under the quasi-static loadings are presented to validate the proposed method. The method provides detailed microscopic stress distribution of the composites under the coupled thermo-mechanical loading for failure analysis, which shows that a higher ambient temperature variation will generally cause stiffness degradation and failure strength for both uniaxially and biaxially loaded laminates.

Numerical simulation of microscopic residual stress evolution in polycrystalline aggregate subjected to weld thermal cycle

Weld residual stress affects joint performance in terms of the fatigue life and resistance to stress corrosion cracking. Thus far, the weld residual stress has been discussed mainly at the scale of the joint—the macroscopic scale. However, the weld residual stress can be inhomogeneous at the microscopic scale like a crystal grain; this aspect has not been discussed well. In this study, a numerical simulation model was developed to calculate the inhomogeneous distribution of the microscopic residual stress, based on the both-ends-fixed bar model. The bar was modeled by a polycrystalline aggregate, and the elastic and plastic anisotropy were defined for each grain. Thermal cycles with various peak temperatures were applied on the both-ends-fixed polycrystalline bar, and the evolution of the microscopic stress was simulated. The elastic and plastic anisotropy of the grains affected the inhomogeneity of the microscopic stress distribution. Elastic anisotropy caused inhomogeneity under elastic loading, whereas plastic anisotropy affected that under plastic loading. It was demonstrated that a microscopic stress higher than the applied macroscopic stress was generated when anisotropy was taken into consideration.

Evaluate the Fatigue Life of CFRC Subjected to Coupled Thermo-Mechanical Loading.

Mechanical properties of composites manufactured by high-temperature polymer polyether ether ketone (PEEK) with continuous reinforced fibers are closely dependent on ambient temperature variations. In order to effectively study fatigue failure behaviors of composites under the coupled thermo–mechanical loading, a well-established microscopic model based on a representative volume element (RVE) is proposed in this paper. Stiffness degradation behaviors of the composite laminates at room and elevated temperatures are firstly investigated, and their failure strengths are compared with experimental data. To describe the fatigue behaviors of composites with respect to complex external loading and ambient temperature variations, a new fatigue equation is proposed. A good consistency between theoretical results and experimental data was found in the cases. On this basis, the temperature cycling effects on the service life of composites are also discussed. Microscopic stress distributions of the RVE are also discussed to reveal their fatigue failure mechanisms.

Numerical Simulation and Microscopic Stress Mechanism for the Microscopic Pore Deformation during Soil Compression

Pore structure is closely related with strength, constitutive relation, consolidation characteristics, and permeability properties of soil. Consequently, improving the understanding of the relationship between microscopic structure and macroscopic physical and mechanical properties has extremely important scientific significance. A large number of studies have shown that pores of soil have fractal features, and hence, the carpet model can be used to approximately simulate the fractal structure of clay. In the present study, ANSYS software was selected to establish a microscopic model of clay to study the distribution of microscopic stress and microscopic deformation characteristics of pores under different consolidation pressures. Besides, the variation law of microscopic pore size was quantitatively determined by using IPP (Image‐Pro Plus) software. Combined with the fractal theory, the changes of microscopic pore of numerical simulation and that of physical experiment during compression of clay are studied. All the results indicated that the microscopic stress distribution of clay is not uniform on the compaction process. The larger the pore size is, the bigger the compression stress on both sides and the greater the bending deformation of upper part of the pore is, which leads to the deformation of larger pores which is bigger than that of smaller pores. Based on the results, issues about the microscopic mechanism of the difference in vertical and horizontal permeability under compression of clay, the relationship between the changes of pore shape and microscopic stress, the preliminary principle of “preferential crush of larger particles” for granular soil, skeleton stress across the region where stiffness is relative larger, and the self‐protection of particles and pores are also discussed. The results of this study are of great importance in understanding of soil compression and related physical and mechanical properties from the microscopic view.

A multi-scale modeling scheme for damage analysis of composite structures based on the High-Fidelity Generalized Method of Cells

This paper presents a description of a multi-scale method to investigate the failure behaviors and damage evolution of composite laminates reinforced with unidirectional fibers. The proposed approach is based on the microscopic mechanical theory and pre-processing function of the ANSYS/LS-DYNA software. At micro-scale, the High-Fidelity Generalized Method of Cells (HFGMC) is employed to establish the microscopic model, which can be used to acquire the microscopic stress distributions in the representative volume element (RVE). Moreover, a viscoplastic constitutive model is employed to describe the nonlinear behaviors of matrix materials. At macro-scale, each integration point in elements is employed to investigate the damage evolution for each lamina. In order to validate the proposed method, the numerical results of failure evolution path and stress-strain responses of the composite laminates are compared with experimental data. A good consistency between theoretical results and experimental data can be found. On this basis, the failure evolution path for each lamina is further investigated. The numerical results revealed that the crack firstly appeared in the 90° lamina. With the further increasing of external loading, the crack will accumulate along with the layer direction for −45° lamina, 45° lamina and 90° lamina.