Strain Energy Research Articles

Effect of Creep, Fatigue and Random Vibration on the Integrity of Solder Joints in BGA Package

This study employs Finite Element Analysis (FEA) to investigate the effects of creep, fatigue, and random vibration on the integrity of solder joints in BGA packages in electronic modules. Evaluating the response of lead-based Sn63Pb37 and lead-free SnAgCu alloy solders (SAC305, SAC387, SAC396, and SAC405) to induced loads - stress, strain, strain energy density, and displacement in the joints is obtained and studied better to understand the mechanism of the joints' degradation. SAC305 and SAC405 are modelled with linear stress-temperature relationships σ = 3.152T–68.167 and σ = 1.543T–34.983, respectively. The magnitude of the strain energy density in the joints is a key failure driver. SAC387 and SAC396 solder joints display lower values of strain energy density and thus have higher durability. Displacement analysis indicates that SAC305 and Sn63Pb37 are prone to deformation-induced failure. SAC387 exhibits the highest fatigue yield stress at 58 MPa, while SAC405 displays the lowest stress at 22 MPa. Analysis of the results of random vibration shows that Sn63Pb37 developed the highest stress at 34.62 MPa and is thus susceptible to stress-induced failure. The robust stress, strain, and strain energy responses of SAC405 and SAC396 provide key insights into improving the mechanical reliability of future electronic devices towards better sustainability.

Quantitative study on fatigue characteristics of warm mix recycled asphalt

The warm mix recycling technology of asphalt pavement can improve the utilization rate of solid waste in highway construction industry on a large scale, and reduce the emission of harmful gases ( NOX, CO2, benzopyrene, etc.) in the process of road construction. It is one of the effective ways to realize carbon neutrality in highway construction industry. The main purpose of this study is to systematically analyze the fatigue characteristics of warm mix recycled asphalt (WMRA) from the perspective of quantitative research, and to provide scientific basis for the popularization and application of this technology. Therefore, this study mainly evaluated the anti-fatigue characteristics of WMRA under different conditions based on the linear amplitude sweeping test ( LAS test). Based on the calculation and analysis of the commonly used fatigue judgment indexes ( stress-strain curve, phase angle-strain curve, S×N curve ( S is the ratio of the instantaneous modulus to the initial modulus of the material, which is often replaced by the virtual modulus in the LAS test, and N is the number of cyclic loadings.), virtual strain storage energy-strain curve), the peak strain of virtual strain storage energy is recommended as the fatigue judgment standard from the perspective of reliability and accuracy, and the peak strain of damage factor is proposed as one of the new fatigue judgment standards. In this paper, the nucleation of microcracks and the coalescence of microcracks are distinguished in the process of fatigue damage evolution, and the peak strain of virtual strain energy storage and the peak strain of damage factor are used as the judging indexes respectively. Finally, based on the theory of continuum damage mechanics, the loss modulus of WMRA is selected as the representative value of material properties to calculate the virtual modulus and damage factor, and the fatigue damage evolution model of WMRA based on the viscoelastic continuum damage model ( VECD model) was constructed. Based on this model, the anti-fatigue characteristics of WMRA with the reclaimed asphalt pavement ( RAP) content were analyzed.

Healthy and diseased tensile mechanics of mouse lung parenchyma

The mechanics of the lung, consisting of high deformation, non-linear, rapid and cyclic loading, remain a critical unknown, hindering advancements in the field despite the pressing urgency of incurable and often fatal pulmonary diseases; such multi-scale ailments impair organ mechanical function by inducing tissue-level alterations. Here, the tensile mechanics of healthy and diseased murine lung parenchyma with induced variable fibrosis and emphysema are compared—exploring multi-rate and directional tissue elasticity and energetics. Remarkably, parenchymal tissue is found to be notably elastic and non-hysteresis prone. Additionally, chronic fibrosis-induced tissues reveal significantly reduced compliance compared to age-matched controls, indicating characteristic stiffening; moreover, maximum stress tends to be greater in exposed than controls. Emphysematous tissues tend to show lower maximum stress than controls, reflective of hallmark tissue destruction and softening. Furthermore, faster loading rate is found to generally yield elevated stiffness and maximum stress, significantly for fibrosis group exposed tissue—this interdependence between loading rate and tissue disease is notable considering the dynamics of breathing. Generally, control tissues are found to be isotropic, as are emphysematous tissues, but fibrosis may lead to increased anisotropy. Additionally, fibrotic and mature-healthy lungs are found to show age effect trends, such as increased strain energy. Along with these findings, this study additionally facilitates future analyses of other diseases by establishing lung biaxial testing protocols for small-scale murine specimens, which can serve as practical and ethical models for exploring human diseases. Overall, this study offers fundamental material characterizations which will enable future formulations of experimentally informed computational models.

Tensile behavior of square-twist origami inspired mechanical metamaterials with soft joints and chirality applications

The performance and behavior of origami-inspired mechanical metamaterials are closely related to their structural design and the joints sub equivalent to the crease, in addition to material selection. Current research on square-twist origami focused on the unidirectional formation between its stable states. However, the complete process of squeezing-folding and stretching-unfolding as well as the mechanical behavior under tensile loading have not been thoroughly studied. In this study, square-twist origami mechanical metamaterials (STOMMs) with soft joints are proposed and investigated. The complete process of typical STOMMs from a flat state to folded stable state by extrusion folding and then returning to a flat state by stretch unfolding is explored using the finite element method. The strain energy and deformation characteristics of STOMMs are revealed at eight special stages during the folding, stable state, and unfolding processes. Additionally, the influence of geometric parameters on strain energy, deformation, and tensile behavior is also investigated. Finally, inspired by origami chirality, combinatorial mechanical metamaterials with self-locking/non-self-locking behavior are proposed and validated for their tensile and self-locking behavior. The studies could provide new content for origami-inspired soft joint mechanical metamaterials in terms of self-locking and load-bearing.

Performance parametric formulation of carbon fiber-reinforced composite locking bone implant plates based on finite-element analysis.

The treatment of Giant Cell Tumor (GCT) in the distal radius poses challenges due to the intricate anatomical features of the bone. It often necessitates the use of long implant plates or the interconnection of multiple short plates after tumor excision. However, the deployment of metal plates may increase the risk of screw loosening and various complications. To address these challenges, this study proposes the adoption of carbon fiber-reinforced PEEK (CFRP) as the base material. As a unique strategy, performance parameters (PP) were developed to compare CFRP implant plates with a Ti-6Al-4V plate using the Finite-element Method. The focus was on four elements: the screw axial force, bone growth, callus formation, and bone resorption. The investigation into the screw axial force involved analyzing the internal force of the screw. The remaining parameters were evaluated using the stress, strain, or elastic energy induced in the bones. The findings showed that the second screw endured the largest screw axial force, measuring 10.16 N under a 90-degree 10-N loading at the translocated bone. The model without a callus exerted a significantly greater force on the screw than the model with a callus, leading to screw loosening in the early stage of treatment. The maximum PP, reached 1.62, was achieved with an angle-ply [456/-456] laminate, featuring a weighting fraction of 0.7 for bone growth and 0.1 for the other parameters. This study provides a generalized methodology for assessing the performances of CFRP implants and offers guidelines for future development in composite implant plate technology.

Decoupling mechanical and chemical effects on energetics of coherent nanoprecipitates with interfacial segregation

Interfacial energetics for coherent interfaces are typically calculated using two key concepts: interfacial energy and coherency strain energy. Although these calculations are well-established in pristine systems, their direct application to doped systems often leads to inaccuracies. This is primarily because foreign solute atoms not only modify interfacial energetics but also introduce additional mechanical and chemical effects within the bulk phases. To address this, our study employs the PSTRESS tag in VASP to simulate equivalent lattice stresses induced by solute atoms without physically incorporating them. This novel approach allows us to isolate the doping energy caused by the solute atoms’ mechanical and chemical effects, thereby enhancing our understanding of the impacts of dopants solely on interfacial energetics. Furthermore, we extend the calculations of interfacial energy and coherency strain energy to doped interfaces, providing a precise and effective evaluation method for both bulk and interfacial energetics in doped systems.

Macro‐meso damage cracking and energy dissipation of rock‐backfill composites: Effect of cyclic disturbance frequency

AbstractThis work aims to reveal the effect of cyclic disturbance frequency, i.e., 0.01, 0.1, 0.5, and 1.0 Hz, on damage cracking and energy dissipation characteristics of rock‐backfill composite structure specimens. Testing results show that fatigue volumetric strain and secant modulus increase with increasing disturbance frequency; low‐frequency disturbance leads to an earlier volume expansion. In addition, the strain energy density increases with increasing disturbance frequency. Most of the energy are dissipated for the specimen under high‐frequency disturbance. Finally, computed tomography scanning reveals the influence of disturbance frequency on failure modes; tensile‐splitting failure and shear failure are likely to occur at the surrounding rock subjected to high‐ and low‐ frequency disturbances. Low‐frequency‐disturbed stress seems easily to stimulate cracks at the rock‐backfill interfaces and the backfill; the backfill can absorb much more energy than high‐frequency circumstances. It is suggested that the role of backfill in energy absorption, contact support, and stress isolation is disturbance frequency dependent.

Robotica: decoupled elastostatic stiffness modeling of hybrid robots

Abstract A decoupling method is proposed for the elastic stiffness modeling of hybrid robots based on the rigidity principle, screw theory, strain energy, and Castigliano’s second theorem. It enables the decoupling of parallel and serial modules, as well as the individual contributions of each elastic component to the mechanism’s stiffness performance. The method is implemented as follows: (1) formulate limb constraint wrenches and corresponding limb stiffness matrix based on the screw theory and strain energy, (2) formulate the overall stiffness matrix of parallel and serial modules corresponding to end of the hybrid robots based on the rigidity principle, principle of virtual work, the wrench transfer formula, and strain energy methods, and (3) obtain and decouple the overall stiffness matrix and deflection of the robot based on the Castigliano’s second theorem. Finally, A planar hybrid structure and the 4SRRR + 6R hybrid robot are used as illustrative examples to implement the proposed method. The results indicate that selectively enhancing the stiffness performance of the mechanism is the most effective approach.

On the Comparative Analysis among Topological Indices for Rhombus Silicate and Oxide Structures

A topological index (TI) is a numeric digit that signalizes the whole chemical structure of a molecular network. TIs are helpful in predicting the bioactivity of molecular substances in investigations of quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR). TIs correlate various chemical and physical attributes of chemical substances such as melting and freezing point, strain energy, stability, temperature, volume, density, and pressure. There are several distance-based descriptors available in the literature, but connection-based TIs are considered more effective than degree-based TIs in measuring the chemical characteristics of molecular compounds. The present study focuses on computing the connection-based TIs for the most significant type of chemical structures, namely, rhombus silicate and rhombus oxide networks. At the end, we compare these structures on the basis of their computed result.

Dynamic Failure Characteristics of Sandstone Containing Different Angles of Pre-Existing Crack Defects

Fracture within the rock is one of the main factors leading to rock destabilization and has a significant effect on the stability of the project. In this study, sandstone is used as a research target, specimens with crack inclination angles of 0°, 30°, 45°, 60°, and 90° are prefabricated, and the split Hopkinson pressure bar (SHPB) impact test of sandstone with cracks is carried out based on digital image recognition technology to explore the dynamic damage characteristics of the specimens with five angles. The basic mechanical parameters of sandstone are tested to determine the RHT model intrinsic parameters, and the numerical computational RHT model of sandstone containing crack defects is established, which is verified in comparison with the test to analyze the validity of the model. Finally, the failure characteristics of the numerical model under initial stress were carried out. The study shows the following: with the increase in the fracture angle, the dynamic compressive strength and deformation modulus are distributed in a slanting V-shape, and the inclination angle of 45° is the smallest. The strain rate and energy dissipation rate are distributed in a slanting N-shape, and the inclination angle of 45° is the largest. The transmittance shows a decreasing trend, which is the opposite of the reflectivity pattern. The crack angle determines the location and direction of the initial crack, which affects the failure mode. In addition, the parameters of the RHT constitutive model suitable for sandstone are obtained, and the damage and strength patterns of the established RHT model are highly consistent with the laboratory test results. The damage range of numerical models for crack defects with different inclination angles is negatively correlated with confining pressure values and positively correlated with axial pressure values. The damage zones are symmetrically distributed approximately perpendicular to the direction of cracks, and the confining pressure has a contributing role in the peak of the element stresses; however, the axial compression has no contribution in the peak of the element stresses.

Numerical simulation of fault activity in the Qilian tectonic belt and dynamic background of Menyuan earthquake series

Some faults in the Qilian tectonic belt are seismogenic areas for strong earthquakes, including the western section of the Lenglongling fault, which frequently occures moderate-strong Menyuan earthquakes. In this study, using GPS velocity data of 1991–2015 as the boundary constraints, a three-dimensional viscoelastic finite element dynamic model is constructed by comprehensively considering the regional dynamic environment, crust-mantle transverse-longitudinal inhomogeneity, and spatial spreading of a complex fault system. The objective is to investigate the long-period characteristics of fault movement and stress change in the Qilian tectonic belt caused by tectonic loading, and to discuss the seismogenic conditions of the Menyuan earthquakes. The results show that the annual change of long-period movement and stress of the major faults in the Qilian Mountain tectonic zone are characterized by significant segmentation. Due to its unique geometric bend morphology, the western section of Lenglongling fault has a low movement rate, significant slip deficit and high shear stress accumulation, which are conducive to the gestation and occurrence of earthquakes. Furthermore, the seismogenic area of the Menyuan earthquake series is jointly subjected to NE-SW compressive and NW-SE tensile stress fields, and the maximum shear stress and elastic strain energy accumulate faster than in the surrounding areas. Overall, the western section of the Lenglongling fault has a strong dynamic background and favorable conditions for the frequent occurrence of the Menyuan earthquake series.

Collapse analysis and robustness assessment of dropped-story steel frame structures based on structural vulnerability theory

ABSTRACT This paper proposes an improved analysis method based on the theory of structural vulnerability, which incorporates structural redundancy and comprehensively analyzes structural vulnerability and robustness by considering the changes in structural stiffness and redundancy after damage to structural members under conventional loading. The improved method takes into account the changes in the strain energy of the structure after the damage of the structural members, which can be more in line with the actual situation of continuity collapse, and solves the complex process of traditional structural vulnerability theory that requires clustering and unclustering, greatly reducing the workload as well as solving the problem of not being able to find the critical members of the structure. The improved method is used to analyze the vulnerability of a 5-story dropped-story steel frame structure, to find the critical members of the structure based on the test data simulated by ABAQUS, to evaluate the robustness, and to propose improvement measures. The results show that the improved vulnerability assessment method is more reasonable and effective and can be applied to different steel frame structures.

Multiscale simulation and experimental studies on modal damping of ultra‐thick CFRP laminates

AbstractThe vibration characterization of ultra‐thick laminates widely used in aerospace and marine industries was different from that of thin laminates. However, modal testing and simulation methods were generally limited to relatively thin laminates. To explore the vibration behavior of ultra‐thick laminates, a novel multiscale simulation technology based on the representative volume modal strain energy (RVMSE) method is presented for predicting modal damping in this paper. The adaptive Greedy‐Based Generation (GBG) algorithm is used to create a 3D random distribution of fibers for composites. Modal shape information of the structure is obtained according to the Lanczos algorithm, which is used as an input parameter for the microscopic model. This is followed by homogenization based on the volumetric analysis performed on representative volume elements (RVEs) to determine the strain energy in six directions. The calculation of modal damping is performed by using the modal strain energy (MSE) method and the damping properties of the six directions. The fast rate of convergence and high accuracy of the method are demonstrated through different examples. The vibration response predictions produced by novel RVMSE methodology are shown to closely match experimental measurements, providing scope to expand the application of this approach to more complex, ultra‐thick laminate components.Highlights The RVMSE method uses a higher level of homogenization to overcome the limitations of the traditional MSE method for calculating the damping of ultra‐thick CFRP laminates. The modal parameter error is controlled to less than 10%, and the experimental results fill the gap of the damping data of ultra‐thick CFRP structure. The proposed RVMSE model improves the accuracy of dynamic response prediction for ultra‐thick laminates.

Uncovering the progressive failure process of primary coal-rock mass specimens: Insights from energy evolution, acoustic emission crack patterns, and visual characterization

The failure and instability of deep coal-rock mass structures, which are influenced by mining disturbances, are major contributors to disasters like rock bursts. This study involved conducting indoor experiments using uniaxial loading test and acoustic emission (AE) experiments on indigenous primary coal-rock mass (PCRM). We utilize chaotic bifurcation based on strain energy to characterize the progressive damage stages of PCRM, demonstrating the chaotic characteristics of energy evolution during the gradual destruction process. The degree of damage resulting from PCRM failure was evaluated by jointly applying P-wave velocity tomography and AE event localization. Additionally, the classification of crack patterns in PCRM was conducted using the RA-AF correlation analysis method. The segmentation boundaries of crack classification patterns were then redefined using the Gaussian mixture model (GMM) algorithm. The research findings indicate that the chaotic bifurcation model of strain energy classifies stress into four stages: the stable region (Ⅰ), the metastable region (Ⅱ), the bifurcation region (Ⅲ), and the chaotic region (Ⅳ). The presence of a low-velocity zone in P-waves may indicate crack accumulation and damage within the system. Additionally, areas with abnormal P-wave velocities exhibit numerous AE events. The crack classification patterns of the four stages undergo an evolution from predominantly tensile cracks to a mixture of tensile and shear cracks, and the GMM algorithm successfully identifies the optimal separation path for crack classification boundaries. We propose an adaptive kernel density estimation (AKDE) algorithm to quantify the spatial distribution of AE events, thus offering a visual representation of the damage patterns at various stages.

Suzuki segregation behavior and mechanism in a Co–Cr–Fe–Ni–Mo high-entropy alloy

The knowledge of the Suzuki effect in compositionally complex CoNiCrMo and CoCrFeNiMo solid-solution alloys is rather limited. In this study, the enrichment of Co and Mo atoms and depletion of Cr, Fe, and Ni atoms were determined within the region of four atomic layers at stacking faults (SFs) in a typical quinary concentrated solid-solution alloy (Co0.95Cr0.8Fe0.25Ni1.8Mo0.475) by using scanning transmission electron microscopy and energy dispersive X-ray spectroscopy. To better understand the Suzuki effect, two-stage first-principles Monte Carlo (MC) simulations each with up to 3000 trial swap steps were performed. First, the simulation results suggested the strong tendency of Mo segregation at the second nearest neighbor (2NN) sites at SFs. Nonetheless, as a further Mo segregation induces the excessively large lattice distortion and intrinsic strain energy, it would be inhibited. It was deemed one potential reason for the finite Mo segregation. Second, the simulations revealed the origin and formation of co-segregation of Co and Mo atoms. The segregated Mo atoms at the 2NN sites attract Co atoms, forming the local D019-type ordering at SFs. As a consequence, the stacking fault energy can reach a strongly negative value below −500 mJ/m2. Meanwhile, the Co/Mo co-segregated SFs have high stability against phase transitions to intermetallics and martensite at 773 K.

Effects of Steel Fiber Content on Compressive Properties and Constitutive Relation of Ultra-High Performance Shotcrete (UHPSC)

Shotcrete is widely used in civil engineering as a supporting structure. In this paper, the compressive behavior of ultra-high-performance shotcrete (UHPSC) with different steel fiber content by volume (0, 0.5%, 0.75%, 1%, 1.25%, 1.5%) was investigated. The results showed that the failure pattern of UHPSC was changed from brittle failure to ductile failure with the increase in steel fiber content. The compressive strength, peak strain and compressive toughness of UHPSC increased with the increase in steel fiber content, but the elastic modulus and Poisson’s ratio did not change significantly. With content of 1.5% steel fibers, its axial compressive strength, peak strain and compressive strain energy were 122.7 MPa, 3749 με and 0.269 MPa, respectively, increased by 14%, 23.5% and 55.5% compared with those without steel fiber. The peak strain and compressive toughness were higher than that of ultra-high-performance concrete (UHPC), while the elastic modulus of UHPSC was lower than that of UHPC. Based on the experimental data, the relationship between compressive strength, peak strain, compressive toughness and the change in the characteristic value of steel fiber content (λf) were revealed. The uniaxial compressive constitutive model of UHPSC with different steel fiber content was established and reflected the change rule of the shape parameter of α (constitutive model ascending section) and β (constitutive model descending section) with λf. The experimental results were in good agreement with the model calculation results, which can provide theoretical support for the structural design of UHPSC.

Vibrations of skew cylindrical shells made of FG-GPLRCs under rapid surface heating

An analysis is performed in this research to examine the thermally induced vibrations in skew cylindrical shells. It is assumed that shell is made from a composite laminated material where each layer is reinforced with graphene platelets (GPLs). The amount of GPLs in the layers may be different which results in a piecewise functionally graded media. The one-dimensional transient heat conduction equation is established through the thickness of the shell. Heat conduction equation is solved using the finite difference method for each layer and continuity of temperature and heat flux is applied between the layers. Crank Nicolson algorithm is implemented to obtain the temperature profile at each time step and after that thermally induced force and moment are evaluated. The kinematics of the shell are estimated following the first order shear deformation shell theory. Also it should be noted that an oblique coordinates system in addition to orthogonal system is defined which make it easier to apply the boundary conditions. The definition of strain and kinetic energies are constructed and Following the Ritz method whose shape functions are estimated by Chebyshev polynomials, energies are provided in discrete form of the governing equations. Results of this study are provided to explore the effects of thermal and mechanical boundary conditions, geometry of the shell, weight fraction and distribution patterns of GPLs. It is highlighted that thermally induced vibrations indeed exist especially in thin class of shells.

Biomechanical evaluation of a sheep tracheal scaffold.

Tissue engineering is a set of techniques for producing or reconstructing tissue that primarily aims to restore or improve the function of tissues in the human body. The aim of the present study was to evaluate the mechanical and histological characteristics of decellularized tracheal scaffolds prepared in comparison with fresh trachea for use in tracheal repair. In order to prepare the scaffold, sheep's trachea was prepared and after cleaning the waste tissues, they were decellularized. Then decellularized scaffolds were evaluated histologically and laboratory and numerical study of the nonlinear mechanical behavior of tracheal tissue and scaffold and their comparison. Examining the results of histological evaluations showed that the decellularization of the scaffolds was completely done. These results were confirmed by hematoxylin-eosin staining. Also, the exact hyperelastic properties of tracheal tissue and scaffold were used in biomechanical models, and according to the presented results, the five-term Mooney-Rivlin strain energy density function became a suitable behavioral model for modeling the hyperelastic behavior of trachea and scaffold. In total, the results of this research showed that the scaffolds obtained from decellularization by preserving the main compositions of the desired tissue can be a suitable platform for investigating cell behaviors.

Feasibility biomechanical study of injectable biphasic calcium phosphate bone cement augmentation of the proximal femoral nail antirotation (PFNA) for the treatment of two intertrochanteric fractures using cadaveric femur.

This study evaluated the feasibility of the femoral bone after fixation using biphasic calcium phosphate cement-augmentation of the proximal femoral nail antirotation (PFNA) compared with PFNA without cement. This study presented to compare the stiffness, fatigue testing, and compressive strength between stable (AO31-A2.1) and unstable (AO31-A3.3) intertrochanteric fractures treated by cement augmented PFNA of the cadaveric femoral. Biphasic calcium phosphate cement was injected to align and compatible with PFNA and the reconstructive procedure was monitored the cement placement using X-ray imaging during operation. The testing demonstrated that the cement could be injected through a small needle (13G, 16cm length, 1.8mm inner diameter) within a suitable operating time. The feasibility study of the biomechanical testing was divided into three tests: stiffness test, fatigue cyclic load, and compression test. The results showed that the cement-augmented specimens exhibited higher stiffness than the control specimens without cement. The cement-augmented specimens also showed lower strain energy during the fatigue test, resulting in higher compressive strength (4730.7 N) compared to the control specimens (3857.4 N). There is a correlation between BMD and fracture load and the increase in compression load of the cement-augmented femoral compared to the controls as well as an increase in strain energy of fatigue cyclic testing was found. Biphasic calcium phosphate cement-augmented of the PFNA biomechanically enhanced the cut-out resistance in intertrochanteric fracture. This procedure is especially efficient for unstable intertrochanteric fracture suggesting the potential benefits of using biphasic calcium phosphate cement in medical applications.

Effect of crack on morphology evolution of the precipitates in Nickel-based superalloys under applied stress

Nickel-based superalloys are widely used in turbine blades and aviation engine due to their outstanding mechanical property at elevated temperatures. The superior mechanical property of nickel-based superalloys is highly relevant to the morphology evolution of γ′ precipitates in the γ matrix phase. At high temperature, the directional coarsening of γ′ precipitates may result in rafting behavior under applied stress. In addition, defects such as the cavities, inclusions and micro-cracks introduced during the manufacturing process in superalloys have significant influence on the evolution of the γ′ precipitates. In this work, a phase field model with crack and precipitate as order parameters has been proposed to investigate the effect of crack on the morphology evolution of the γ′ precipitates. The morphology evolution and volume fraction evolution of the γ′ precipitates in the Nickel-based superalloys with different cracks have been investigated under the tensile and shear stresses. It is found that the local high equivalent stress and high elastic strain energy near the crack lead to the migration of solute atoms from the high stress region to the low stress region. The migration of solute atoms results in the disappearance of the γ' phases in the vicinity of cracks, which is consistent with the experimental observation. The disappearance of the γ' phases around the crack reduces the volume fraction of the γ′ precipitates, which will affect the mechanical property of the superalloys.