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Scholars mainly propose and establish theoretical models of cumulative fatigue damage for their research fields. This review aims to select the applicable model from many fatigue damage models according to the actual situation. However, relatively few models can be generally accepted and widely used.

This review introduces the development of cumulative damage theory. Then, several typical models are selected from linear and nonlinear cumulative damage models to perform data analyses and obtain the fatigue life for the metal.

Considering the energy law and strength degradation, the nonlinear fatigue cumulative damage model can better reflect the fatigue damage under constant and multi-stage variable amplitude loading. In the following research, the complex uncertainty of the model in the fatigue damage process can be considered, as well as the combination of advanced machine learning techniques to reduce the prediction error.

This review compares the advantages and disadvantages of various mainstream cumulative damage research methods. It provides a reference for further research into the theories of cumulative fatigue damage.

The stress state near the notch affects fatigue damage directly, but quantifying the stress field is difficult. The purpose of this study is to provide a mathematical description method of the stress field near the notch to achieve a reliable assessment of the fatigue life of notched specimens.

Firstly, the stress distribution of notched specimens of different materials and shapes under different stress levels is investigated, and a method for calculating the stress gradient impact factor is presented. Then, the newly defined stress gradient impact factor is used to describe the stress field near the notch, and an expression for the stress at any point along a specified path is developed. Furthermore, by combining the mathematical expressions for the stress field near the notch, a multiaxial fatigue life prediction model for notched shaft specimens is established based on the damage mechanics theory and closed solution method.

The stress gradient factor for notched specimens with higher stress concentration factors (V60-notch, V90-notch) varies to a certain extent when the external load and material change, but for notched specimens with relatively lower stress concentration factors (C-notch, U-notch, stepped shaft), the stress gradient factor hardly varies with the change in load and material, indicating that the shape of the notch has a greater influence on the stress gradient. It is also found that the effect of size on the stress gradient factor is not obvious for notched specimens with different shapes, there is an obvious positive correlation between the normal stress gradient factor and the normal stress concentration factor compared with the relationship between the shear stress gradient factor and the stress concentration factor. Moreover, the predicted results of the proposed model are in better agreement with the experimental results of five kinds of materials compared with the FS model, the SWT model, and the Manson–Coffin equation.

In this paper, a new stress gradient factor is defined based on the stress distribution of a smooth specimen. Then, a mathematical description of the stress field near the notch is provided, which contains the nominal stress, notch size, and stress concentration factor which is calculated by the finite element method (FEM). In addition, a multiaxial fatigue life prediction model for shaft specimens with different notch shapes is established with the newly established expressions based on the theory of damage mechanics and the closed solution method.

The effect of bolt stripping failure on the ductility of steel end plate beam-column connections has received relatively little investigation to date. The objective with the present work is to establish a validated numerical model of end plate connections at elevated temperatures, which predicts the mechanical behaviour and failure modes observed in the experimental tests including the bolt stripping failure. Furthermore, the validated FE model was used to investigate the effect of stripping failure on both the rotational and load-bearing capacity of end plate connection.

The analysis was conducted on a validated numerical model of end plate connections at elevated temperatures, which predicts the mechanical behaviour and failure modes observed in the experimental tests including the bolt stripping failure. The material was modelled considering ductile damage initiation and evolution featured in ABAQUS/Standard.

This study demonstrates that thick end plates can prevent stripping failure which significantly improves the rotational capacity of the connection. This failure mode can develop readily with thin end plates; however the effect is often unrealistically mitigated through idealised experimental tests. The rotational capacity of a connection can be 5.0 times higher if stripping failure is avoided, particularly at elevated temperatures. Eurocode 3 part 1.8 does not consider the possibility of stripping failure when discussing the requirements for plastic analysis. It is concluded in the present study that by allowing for the possibility of bolt stripping, the mode of failure can often shift from end plate failure to bolt stripping, this in turn significantly reduces the connection rotational capacity.

The effect of bolt stripping failure on the ductility of steel end plate beam-column connections has received relatively little investigation to date.

Engineering composite laminates/structures are usually subjected to complex and variable loads, which result in interlayer delamination damage. However, damaged laminate may cause the whole structure to fail before reaching the design level. Therefore, the purpose of this paper is to develop an equivalent model to effectively evaluate compressive residual strength.

In this paper, taking carbon fiber reinforced composite T300/69 specimens as the study object, first, the compressive residual strength under different impact energy is obtained. Then, zero-thickness cohesive elements, Hashin failure criteria and Camanho nonlinear degradation scheme are used to simulate the full-process simulation for compression after edge impact (CAEI). Lastly, based on an improved Whitney–Nuismer criterion, the equation of edge hole stress distribution, characteristic length and compressive residual strength is used to verify the correctness of the equivalent model.

An equivalent relationship between the compressive residual strength of damaged laminates and laminates with edge hole is established. For T300/69 laminates with a thickness of 2.4 mm, the compressive residual strength after damage under an impact energy of 3 J is equivalent to that when the hole aperture R = 2.25 mm and the hole aperture R = 9.18 mm when impact energy is 6 J. Besides, the relationship under the same size and different thickness is obtained.

The value of this study is to provide a reference for the equivalent behavior of damaged laminates. An equivalent model proposed in this paper will contribute to the research of compressive residual strength and provide a theoretical basis for practical engineering application.

There have been limited investigations on the mechanical characteristics of tunnels supported by corrugated plate structures during fault dislocation. The authors obtained circumferential and axial deformations of the spiral corrugated pipe at various fault displacements. Lastly, the authors examined the impact of reinforced spiral stiffness and soil constraints on the support performance of corrugated plate tunnels under fault displacement.

By employing the theory of similarity ratios, the authors conducted model tests on spiral corrugated plate support using loose sand and PVC (polyvinyl chloride) spiral corrugated PE pipes for cross-fault tunnels. Subsequently, the soil spring coefficient for tunnel–soil interaction was determined in accordance with ASCE (American Society of Civil Engineers) specifications. Numerical simulations were performed on spiral corrugated pipes with fault dislocation, and the results were compared with the experimental data, enabling the determination of the variation pattern of the soil spring coefficient.

The findings indicate that the maximum axial tensile and compressive strains occur on both sides of the fault. As the reinforced spiral stiffness reaches a certain threshold, the deformation of the corrugated plate tunnel and the maximum fault displacement stabilize. Furthermore, a stronger soil constraint leads to a lower maximum fault displacement that the tunnel can withstand.

In this study, the calculation formula for density similarity ratio cannot be taken into account due to the limitations of the helical corrugated tube process and the focus on the deformation pattern of helical corrugated tubes under fault action.

This study provides a basis for the mechanical properties of helical corrugated tube tunnels under fault misalignment and offers optimization solutions.

In this paper, an attempt is made to obtain buckling loads, ultimate bearing capacity and other required structural characteristics of grid structure panels. The numerical method for post-buckling behavior analysis of panels involving multiple invisible damages is also presented.

In this paper, two bidirectional stiffened composite panels are manufactured and tested. Multiple discrete invisible damages are introduced in different positions of the stringers, and the experimental and simulation investigation of buckling and post-buckling were carried out on the damaged stiffened panels.

The simulation load–displacement curves are compared with the experimental results, and it is found that the simulation model can well predict the occurrence of buckling and failure loads. The strain curve shows that the rate of strain change at the damaged site is greater than that at the undamaged site, which reflects that the debond is more likely occurred at the damaged site. The simulation verifies that the panel is usually crushed due to matrix compression and fiber–matrix shear.

In this paper, post-buckling tests and numerical simulations of bidirectional stiffened composite panels with impact damage were carried out. Two panels with four longitudinal stringers and two transverse stringers were manufactured and tested. The buckling and post-buckling characteristics of the grid structure are obtained, and the failure mechanism of the structure is explained. This is helpful for the design of wall panel structure.

The purpose of this study is to develop an efficient numerical procedure for simulating the effect of printing orientation, as one of the primary sources of anisotropy in 3D-printed components, on their fracture properties.

The extended finite element method and the cohesive zone model (XFEM-CZM) are used to develop subroutines for fracture simulation. The ability of two prevalent models, i.e. the continuous-varying fracture properties (CVF) model and the weak plane model (WPM), and a combination of both models (WPM-CVF) are evaluated to capture fracture behavior of the additively manufactured samples. These models are based on the non-local and local forms of the anisotropic maximum tangential stress criterion. The numerical models are assessed by comparing their results with experimental outcomes of 16 different configurations of polycarbonate samples printed using the material extrusion technique.

The results demonstrate that the CVF exaggerates the level of anisotropy, and the WPM cannot detect the mild anisotropy of 3D-printed parts, while the WPM-CVF produces the best results. Additionally, the non-local scheme outperforms the local approach in terms of finite element analysis performance, such as mesh dependency, robustness, etc.

This paper provides a method for modeling anisotropic fracture in 3D-printed objects. A new damage model based on a combination of two prevalent models is offered. Moreover, the developed subroutines for implementing the non-local anisotropic fracture criterion enable a reliable crack propagation simulation in media with varying degrees of complication, such as anisotropy.

Research on strategic alliances is concerned with two issues: continuation and reconfiguration. Building on prior research that examines the two issues separately, the paper studies them simultaneously. This paper aims to investigate how strategic alliances may exert the synergetic effect between dynamics and stability as well as to discuss the dynamic evolution process and influence factors of strategic alliances.

This paper describes the construction of a two-party evolutionary game model of alliance and partners. The model is used to analyze the evolution process of synergetic mechanism to determine when to terminate and when to continue with a partnership. Further, numerical simulation is used to quantify the results and to gain insight into the effects of various factors on the dynamic evolution of the synergetic mechanism.

This paper reveals several synergetic states of dynamics and stability in the alliances. The results show that synergy states are positively affected by the collaborative innovation benefits, alliance management capability, the intensity of intellectual property protection, liquidated damages and reputation losses, and negatively affected by the absorptive capacity of partners.

The study helps the alliance to achieve long-term development as well as to balance the paradoxical relationship. The results suggest that managers of strategic alliances should focus on building strong and long-term relationships in order to achieve high performance innovations. Managers should also pay close attention to their partners’ behaviors in previous alliances.

This paper provides new insights into the paradoxical relationship in alliance by revealing the evolution of synergetic mechanism between dynamics and stability. The results remind alliances to understand the relationship between dynamics and stability and to notice the influence factors of synergistic effects when they are making decisions.

The purpose of this study is to describe the mechanism of single-crystal high-temperature creep deformation, predict the creep life more accurately and study the creep constitutive and lifetime models with microstructure evolution.

The mechanical properties of nickel-based single-crystal superalloy are closely related to the γ' phase. Creep tests under four different temperature and stress conditions were carried out. The relationship between creep temperature, stress and life is fitted by numerical method, and the creep activation energy is obtained. The creep fracture surface, morphology and evolution of strengthening phase (γ') and matrix phase (γ) during different creep periods were observed by scanning electron microscope. With the increase of creep temperature, the rafting time is advanced. The detailed morphology and evolution of dislocations were observed by transmission electron microscope (TEM).

With the increase of creep temperature, the rafting time is advanced. The detailed morphology and evolution of dislocations were observed by TEM. Dislocations are mainly concentrated in the γ channel phase, especially at high temperature and low stress.

A creep constitutive model based on the evolution of γ' phase size and γ channel width was proposed. Compared with the experimental results, the predicted creep life is within 1.4 times error dispersion band.

Regeneratively cooled thrust chamber is a key component of reusable liquid rocket engines. Subjected to cyclic thermal-mechanical loadings, its failure can seriously affect the service life of engines. QCr0.8 copper alloy is widely used in thrust chamber walls due to its excellent thermal conductivity, and its mechanical and fatigue properties are essential for the evaluation of thrust chamber life. This paper contributes to the understanding of the damage mechanism and material selection of regeneratively cooled thrust chambers for reusable liquid rocket engines.

In this paper, tensile and low-cycle fatigue (LCF) tests were conducted for QCr0.8 alloy, and a Chaboche combined hardening model was established to describe the elastic-plastic behavior of QCr0.8 at different temperatures and strain levels. In addition, an LCF life prediction model was established based on the Manson–Coffin formula. The reliability and accuracy of models were then verified by simulations in ABAQUS. Finally, the service life was evaluated for a regenerative cooling thrust chamber, under the condition of cyclic startup and shutdown.

In this paper, a Chaboche combined hardening model was established to describe the elastoplastic behavior of QCr0.8 alloy at different temperatures and strain levels through LCF experiments. The parameters of the fitted Chaboche model were simulated in ABAQUS, and the simulation results were compared with the experimental results. The results show that the model has high reliability and accuracy in characterizing the viscoplastic behavior of QCr0.8 alloy.

(1)The parameters of a Chaboche combined hardening constitutive model and LCF life equation were optimized by tensile and strain-controlled fatigue tests of QCr0.8 copper alloy. (2) Based on the Manson–Coffin formula, the reliability and accuracy of constitutive model were then verified by simulations in ABAQUS. (3)Thermal-mechanical analysis was carried out for regeneratively cooled thrust chamber wall of a reusable liquid rocket engine, and the service life considering LCF, creep and ratcheting damage was analyzed.