Smoothed Particle Hydrodynamics Finite Element Research Articles

Morphological study of cortical bone damage caused by high-pressure water jet erosion based on SPH-FEM coupling algorithm

Currently, traditional processing methods such as drilling, sawing, and milling are primarily utilized in orthopedic surgery, generating a significant amount of heat during the cutting process, leading to irreversible damage to bone and surrounding tissues. High-pressure water jet technology has demonstrated the capability to effectively reduce cutting temperatures and prevent thermal damage during the cutting process. It holds promising potential as an alternative approach to traditional surgical techniques in orthopedic surgery. This study selected the SPH-FEM (Smoothed particle hydrodynamics-Finite element method) coupling algorithm and LS-DYNA software to simulate the effects of high-pressure water jet erosion on cortical bone. The study analyzed the impact of jet pressure on damage morphology and the degree of cortical bone breakage. The simulation results indicate that the concave section of cortical bone damaged by high-pressure water jet is “U” shape. The maximum damage depth of cortical bone increases with the increase in jet pressure. Specifically, as jet pressure increases from 80 MPa to 245 MPa, the increase rate of the average cortical bone damage depth increased from about 0.01 mm/s to more than 0.45 mm/s. The beginning of the concave section of cortical bone damage presents a “funnel” shape, and the width of cortical bone damage reaches its maximum. When the jet pressure is below 180 MPa, there is a significant fluctuation in the width of cortical bone damage. However, with increasing jet pressure, the fluctuation lessens. Physical experiments were carried out under identical technological parameters to verify the numerical results. The experimental results are basically consistent with the numerical results, which can provide a theoretical basis for improving the surface quality of jet erosion of cortical bone.

Deflecting asteroid Itokawa by subsurface explosion: Effect of explosion position on asteroid angular velocity change

Explosion deflection has recently become an important topic in hazardous asteroid deflection. Changes in asteroid velocity and angular velocity, as well as the degree of structural damage, should be fully considered in the explosion deflection scheme. This study investigates the effect of explosion position on the deflection of the asteroid 25143 Itokawa. First, we propose a mathematical model to quickly determine the changes in the angular velocity of Itokawa with explosions at different positions, and verified its reliability through numerical simulations. Mathematical model indicated a maximum 349-fold difference in Itokawa's angular velocity change under explosions at different positions, and revealed that the decisive factor is the force arm (maximum 850-fold difference), not the moment of inertia (maximum 4.01-fold difference). Then, to demonstrate the effect of porosity on shock wave propagation, we established a mesoscopic model based on the porosities of Itokawa's head and body. We used the single-material arbitrary Lagrangian-Eulerian (ALE) and finite element-smoothed particle hydrodynamics (FE-SPH) adaptive methods to simulate the deflection of the asteroid with a 300-kt TNT-equivalent explosion at different positions 10 m underground. The simulated changes in asteroid velocity and angular velocity were consistent with the predictions of the mathematical model. Finally, we investigated the effects of the asteroid geometry and material composition on the shock wave propagation and asteroid damage evolution (material response and structural response).

An improved composite impact damage model and bird-striking damage analysis with smoothed particle hydrodynamics-finite element method

An improved impact damage model is proposed, which can be used to analyze the progressive failure behavior of fiber-reinforced composites. The model is constructed based on the 3D Hashin failure criterion. However, the difference is that the strain component along the thickness direction in the matrix energy evolution model is introduced, and the effects of and on impact damage are added. Rigid-body and bird-body impact problems are studied, which validates the accuracy of the numerical model by comparison with experiments. A 3D numerical model of light aircraft fuel tank impact is constructed, and the SPH-FEM coupling method is used to predict the bird strike failure problem. The structural damage and impact behavior of a light aircraft fuel tank under impact loading are analyzed. The results show that, under different impact energies, the damage to the matrix is more serious and expands along the fiber direction, and the structure presents different damage forms. This paper provides an effective research model for the study of drop shock and the airworthiness of composite fuel tanks.

Simulations of the interaction between fiber bundles/yarns and the energy absorption of the fabric under hypervelocity impact

In this work, the interaction between fiber bundles/yarns and the energy absorption of the multiple fabrics under hypervelocity impact (HVI) are studied by numerical simulation and experiments. In numerical model, an anisotropic elastic-plastic constitutive equation coupled with the Mie-Grüneisen equation of state (EOS) is adopted to describe deviatoric deformation and strongly nonlinear volumetric compression induced by HVI. Considering the internal interactions within fabrics that possess a hierarchical structure and the evolution of impact-induced debris clouds, a meso‑scale model for woven fabrics is developed using the finite element-smoothed particle hydrodynamics (FEM-SPH) adaptive method. The meso‑scale fabric model is validated through HVI experiments, and the simulation results demonstrate excellent agreement with the experimental data. Notably the model reveals an approximately linear increase relationship between the absorbed energy by the fabric and the impact energy of the projectile. Moreover, the meso‑scale fabric model exhibits enhanced predictive capability in modeling the movement and dispersion of debris clouds. Furthermore, the results of the sensitivity analysis of yarn partition indicate that the model is capable of capturing the interactions between fiber bundles/yarns within the fabric during HVI. With increasing impact velocity, the impact time decreases, which reduces the interaction between fabric components and subsequently leading to a decrease in the generated frictional energy.

Dynamic Response Analysis of Projectile Target Penetration Based on an FE-SPH Adaptive Coupling Method

The penetration of projectiles into targets has a broad background in engineering. In this work, numerical simulations of the projectile-target penetration problem are conducted using the Finite Element Method (FEM), the Smoothed Particle Hydrodynamics (SPH) and the Finite Element–Smoothed Particle Hydrodynamics Adaptive Coupling Method (FE-SPH ACM) based on the LS-DYNA software package. First, the penetration experiments using aluminum targets and ceramic targets are simulated. The experimental and simulation results show that the FE-SPH ACM has the better accuracy in calculating the debris cloud head velocity and interface velocity, with an error of no more than 4%. Furthermore, we use the FE-SPH ACM to investigate the anti-penetration performance of aluminum/ceramic composite targets in different combinations. We find that the reasonable layout can improve the protective performance of multi-layered target, especially composite target plates with ceramic as the front layer. In addition, the ballistic limit velocities for ceramic-aluminum ratios of 3/7, 5/5 and 7/3 are approximately 1300 m/s, 1400 m/s and 1500 m/s, respectively. Obviously, increasing the proportion of ceramic materials can enhance the anti-penetration performance.

Coupled FEM-SPH simulation of the protective properties for metal/ceramic composite armor

To support the structural optimization design of metal-ceramic armor against penetration protection performance, this paper optimizes the armor in terms of protection material, armor structure, and bullet resistance mechanism, and envisages a new metal-constrained ceramic composite armor, which overcomes the disadvantages of ceramic material fragility. A coupled finite element-smooth particle hydrodynamics (FEM-SPH) algorithm is used to simulate the penetration process, and the influence of ceramic unit shape and size on the armor protection performance is investigated by quantitatively comparing the bullet energy loss, velocity change, penetration depth, and other indicators that reflect the ballistic protection mechanism. The results show that metal-confined ceramic armor has repairable performance, and filling ceramic units can reduce armor failure area, save armor repair time, and extend armor service life. When the velocity of the projectile is less than 500 m/s, the damaged area of the armor filled with small-sized unit ceramics (1/4 bullet caliber) is small and easy to repair; when the velocity of the projectile is greater than 500 m/s, the armor filled with large-sized unit ceramics (2 times the bullet caliber) can effectively increase the bullet residence time and improve the armor's resistance to elasticity. The results of this paper can provide a reference for the optimal design of the armor structure.

Numerical Study on Asteroid Deflection by Penetrating Explosion Based on Single-Material ALE Method and FE-SPH Adaptive Method

An asteroid impact can potentially destroy life on this planet. Therefore, asteroids should be prevented from impacting the Earth to impede severe disasters. Nuclear explosions are currently the only option to prevent an incoming asteroid impact when the asteroid is large or the warning time is short. However, asteroids exist in an absolute vacuum, where the explosion energy propagation mechanism differs from that in an air environment. It is difficult to describe this process using standard numerical simulation methods. In this study, we used the single-material arbitrary Lagrangian–Eulerian (ALE) method and the finite element-smoothed particle hydrodynamics (FE-SPH) adaptive method to simulate the process of deflecting hazardous asteroids using penetrating explosions. The single-material ALE method can demonstrate the expansion process of explosion products and energy coupling in absolute vacuum. The FE-SPH adaptive method can transform failed elements into SPH particles during the simulation, avoiding system mass loss, energy loss, and element distortion. We analyzed the shock initiation and explosion damage process and obtained an effective simulation of the damage evolution, stress propagation, and fragment distribution of the asteroid. In addition, we decoupled the penetrating explosion into two processes: kinetic impact and static explosion at the impact crater. The corresponding asteroid damage modes, velocity changes, and fragmentation degrees were simulated and compared. Finally, the high efficiency of the nuclear explosion was confirmed by comparing the contribution rates of the kinetic impact and nuclear explosion in the penetrating explosion scheme.

Numerical modeling of the erosion of alumina particulate reinforced epoxy-matrix composites: Material removal mechanisms including reinforcement fracture

Sacrificial composite coating layers are used to protect surfaces from solid particle erosion due to the high-speed impact of particles. Epoxy-based coatings are easily reapplied and are sometimes mixed together with a reinforcing phase consisting of ceramic particles in an attempt to lower the erosion rate. Previous experiments have indicated that different erosion mechanisms can occur depending on, amongst other things, the relative sizes of the reinforcement and abrasive particles. In the present work, a coupled finite element/smoothed particle hydrodynamics (FE/SPH) decomposition method was used to model the erosion of an epoxy-matrix composite reinforced with relatively large 0.5 mm alumina (Al2O3) spheres, by irregularly shaped 152 μm silicon carbide (SiC) abrasives. 5600 overlapping impacts of SiC particles were modeled on carefully chosen representative volumes of the particulate reinforced composite. A Johnson–Holmquist material model (JH-2) with dynamic tensile strength was used to model the particulate phase, while the epoxy was modeled using a piecewise linear plasticity material model coupled with a Cowper-Symonds strain and strain rate hardening relationship. Realistic abrasive particle morphologies were modeled, based on measurements of the abrasive powder used in the verifying experiments. The erosion rates at both perpendicular and oblique incidence were successfully predicted to within ∼10% of those measured. Both the model and experiments showed that the erosion resistance of the composite was higher than the epoxy at oblique incidence; however, at perpendicular incidence, even though the erosion rate of the reinforcements (0.67 ± 0.04 mm3/g) was lower than that of the epoxy (1.27 ± 0.1 mm3/g), the erosion rate of the composite was slightly higher (∼1.38 ± 0.16 mm3/g) than that of the epoxy. It was shown that this occurred because, as the epoxy eroded in a typically ductile fashion with cutting and ploughing mechanisms, the reinforcements fractured leading to an approximately level eroded surface at any instant. The model was able to capture these material removal mechanisms which were also confirmed using non-contact profilometry of the eroded surfaces.

Experimental characterisation and numerical simulation of ballistic penetration of columnar ceramic/fiber laminate composite armor

To improve the design of lightweight, high-performance bulletproof armors, three columnar ceramic/fiber laminate composite armors were designed and prepared, and their ballistic behavior against 7.62 mm armor-piercing bullets was investigated. Through the microcomputed tomography (micro-CT) analysis of target samples, B4C ceramics were found to exhibit better comprehensive bulletproof properties than SiC ceramics, with a 142 % improvement in the protection margin. The design realized by combining ultra-high-molecular-weight polyethylene (UHMWPE) with aramid III could help decrease the backface signature (BFS) by 53 %. A numerical simulation model was established by combining the smoothed particle hydrodynamics (SPH) and finite element (FE) method, called the SPH–FE method, considering the strain rate effect. The SPH–FE model could accurately describe the damage morphology and contribution of the ceramics in terms of the energy dissipation. The damage radius of the ceramic layer was effectively constrained by the design of the columnar ceramic. The maximum error of the SPH–FE model was 6.41 %. The damage mechanism of each layer of the composite armor in the penetration process was explored in detail. A transition from shear damage to tensile damage occurred with layering as the transition marker.

Debris cloud structure and hazardous fragments distribution under hypervelocity yaw impact

This study investigates how the debris cloud structure and hazardous fragment distribution vary with attack angle by simulating a circular cylinder projectile hypervelocity impinging on a thin plate using the finite element–smoothed particle hydrodynamics (FE-SPH) adaptive method. Based on the comparison and analysis of the experimental and simulation results, the FE-SPH adaptive method was applied to address the hypervelocity yaw impact problem, and the variation law of the debris cloud structure with the attack angle was obtained. The screening criterion of the hazardous fragment at yaw impact is given by analyzing the debris formation obtained by the FE-SPH adaptive method, and the distribution characteristics of hazardous fragments and their relationship with the attack angle are given. Moreover, the velocity space was used to evaluate the distribution range and damage capability of asymmetric hazardous fragments. The maximum velocity angle was extended from fully symmetrical working conditions to asymmetrical cases to describe the asymmetrical debris cloud distribution range. In this range, the energy density was calculated to quantitatively analyze how much damage hazardous fragments inflict on the rear plate. The results showed that the number of hazardous fragments generated by the case near the 35° attack angle was the largest, the distribution range was the smallest, and the energy density was the largest. These results suggest that in this case, debris cloud generated by the impact had the strongest damage to the rear plate.

Numerical study on the dynamic fracture of explosively driven cylindrical shells

Research on the expansion and fracture of explosively driven metal shells has been a key issue in weapon development and structural protection. It is important to study and predict the failure mode, fracture mechanism, and fragment distribution characteristics of explosively driven metal shells. In this study, we used the finite element-smoothed particle hydrodynamics (FE-SPH) adaptive method and the fluid–structure interaction method to perform a three-dimensional numerical simulation of the expansion and fracture of a metal cylindrical shell. Our method combined the advantages of the FEM and SPH, avoiding system mass loss, energy loss, and element distortion; in addition, the proposed method had a good simulation effect on the interaction between detonation waves and the cylindrical shell. The simulated detonation wave propagation, shell damage morphology, and fragment velocity distribution were in good agreement with theoretical and experimental results. We divided the fragments into three regions based on their shape characteristics. We analyzed the failure mode and formation process of fragments in different regions. The numerical results reproduced the phenomenon in which cracks initiated from the inner surface and extended to the outer surface of the cylindrical shell along the 45° or 135° shear direction. In addition, fragments composed of elements are identified, and the mass and characteristic lengths of typical fragments at a stable time are provided. Furthermore, the mass and size distribution characteristics of the fragments were explored, and the variation in the fitting results of the classical distribution function under different explosion pressures was examined. Finally, based on mathematical derivation, the distribution formula of fragment velocity was improved. The improved formula provided higher accuracy and could be used to analyze any metal cylindrical shells with different length-to-diameter ratios.

Analysis of the application of fuselage skin reinforcements with beam element representations in flexible full aircraft models for ditching simulations

The aim of this paper is the application of beam element representations for structural skin reinforcements in flexible full aircraft FE models used in ditching simulations. To verify this approach, it was initially analyzed on flexible reinforced bottom-aircraft panels under guided ditching conditions, considering also structural mesh size variations and partly corresponding fluid mesh densities. For this analysis two different numerical methods were used for comparisons, the coupled Finite Element-Smoothed Particle Hydrodynamics and the Arbitrary Lagrangian Eulerian methods. For the generation of the full aircraft model a multidisciplinary process chain approach and a standardized data format description are used. The beam element representations are considered for the modelling of skin reinforcement as well as other structures like cabin and cargo floor structures. By this approach, first time feasible full aircraft ditching simulations and the subsequent analysis of both global kinematics and the local fuselage structural response could be achieved.

A study of innovative cut blasting for rock roadway excavation based on numerical simulation and field tests

Drilling and blasting is a common excavation method in underground engineering. In modern mine construction, improving the efficiency of rock roadway excavation is a significant issue. With the development of blasting practices and the deepening technical understanding, it is difficult to implement deep-hole blasting with traditional drilling and blasting. The reason is that conventional cut blasting makes it difficult to fully throw out rock masses and create enough free surface. In this paper, an innovative cut blasting technology based on cavity cutting and fragment throwing (CCFT) is studied. It overcomes the limitation of dense hole layout, but strengthens the charge at the bottom, and forms a more sufficient cut cavity through a two-stage explosion. Based on the above ideas, a parallel cut with a double fragment-throwing hole (P-DFH) was designed for the excavation of rock roadways. The effects of CCFT cut blasting were studied at the mesoscopic and macroscopic levels. The smoothed particle hydrodynamics-finite element method (SPH-FEM) was used to establish a P-DFH model. The mechanism of cut cavity formation was studied. The arbitrary Lagrange-Euler with erosion algorithm (ALE-EROSION) was used to establish a global geological model for roadway excavation, and the evolution of rock failure in stages was analyzed. Finally, a field test was conducted to verify the effectiveness of the CCFT technique through monitoring. The application of the CCFT technique has achieved significant results for improving face advance, protecting surrounding rock, and controlling blasting vibration.

Hypervelocity impact on honeycomb structure reinforced with bi-layer ceramic/aluminum facesheets used for spacecraft shielding

In this paper, the honeycomb sandwich panel (HSP) reinforced with bi-layer Ceramic (B4C)/Aluminum (Al7075-T6) facesheets is proposed to be used as a shield for spacecraft against meteoroid orbital debris. A modeling strategy based on Lagrange Finite Element-Smoothed Particle Hydrodynamics (FEM-SPH) coupled method to predict the damage characteristics and the hole morphology is presented for the proposed shielding subjected to hypervelocity impact. The results show good agreement with the experimental data. Based on this investigation, significant improvement in resistance capacities is obtained using the bi-layer B4C/Al7075-T6 facesheets compared to monolayer concepts for HSP.

Theoretical and numerical investigation of deep-hole cut blasting based on cavity cutting and fragment throwing

Cut blasting is the key of single-face blasting in underground rock engineering, which determines the success or failure of the blasting process. Traditional cut blasting is not suitable for deep-hole blasting engineering because of the difficulty of throwing rock fragments and the accumulation at the bottom. In this paper, an advanced concept of cavity cutting and fragment throwing (CCFT) for cut blasting is proposed, which is divided into the following two blasting processes: cut hole breaking and fragment-throwing hole throwing. By establishing a mechanical model of CCFT, cut cavity efficiency is introduced as an evaluation index of the cutting effect, and the advantages of CCFT cut blasting are analyzed theoretically. Based on the smoothed particle hydrodynamics-finite element method (SPH-FEM), a CCFT cut blasting model and a traditional cut blasting model are established and compared. The results show that the detonation of the central fragment-throwing hole in CCFT cut blasting plays a key role in the throwing of rock fragments, improving the cut cavity efficiency by approximately 20%. Additionally, 9 sets of numerical models are established to study the effects of various parameters on the cut cavity formation, and optimization suggestions are given for the parameters. The findings show that as the hole depth increases, more blasting energy is needed for the throwing of rock fragments, which can be effectively achieved by increasing the ratio of the charge weight δ. The hole spacing needs to be properly designed to ensure that the rock between the holes is penetrated and broken. The large-diameter fragment-throwing hole guides the development of blasting cracks and promotes rock fragmentation. Finally, two engineering cases, namely, one-step shaft excavation and deep-hole drilling and blasting in a rock tunnel, illustrate the application of CCFT cut blasting. The good application results provide references for similar engineering projects.

Analysis of fuselage skin reinforcements with beam element models in flexible aircraft panels for ditching simulations

This paper is dedicated to the use of beam element models for skin structural reinforcements in guided ditching simulations with a flexible aircraft panel. This approach was analysed by means of finite element simulations of the structure subjected to a constant pressure load and guided ditching loading conditions. To verify this approach, finite element models of different discretization types and different mesh sizes were considered in the computations. Moreover, guided ditching simulations were enhanced by comparisons with the coupled Finite Element-Smoothed Particle Hydrodynamics and the Arbitrary Lagrangian Eulerian methods.

Seismic Analysis of a Large LNG Tank Considering Different Site Conditions

Seismic resilience of critical infrastructure, such as liquefied natural gas (LNG) storage tanks, is essential to the safety and economic well-being of the general public. This paper studies the effect of different ground motions on large LNG storage tanks under four different site conditions. Key parameters of structural design and dynamic analysis, including von Mises stress of outer and inner tanks, tip displacement, and base shear, are analyzed to directly evaluate the safety performance of the large LNG tanks. Because the size of an LNG tank is too large to perform any experiments on a physical prototype, Smoothed Particle Hydrodynamics-Finite Element Method (SPH-FEM) simulation is used as a feasible and efficient method to predict its seismic response. First, the accuracy of the SPH-FEM method is verified by comparing sloshing frequencies obtained from theoretical formulation to experimental results and SPH-FEM models. Then, the seismic response of a real-life 160,000 m3 LNG prestressed storage tank is evaluated with different liquid depths under four site classes. Simulation results show that the tip displacements of the LNG tank at liquid levels of 25% and 50% under site class IV are nearly identical to that of 75% and 100% under site class II. In addition, the maximum von Mises stress of the inner tanks exceeds 500 MPa in all four site classes and jeopardizes the structural integrity of large LNG tanks. As a result, optimization of structural design and the establishment of an early warning system are imperative to the safety of LNG tanks at high liquid levels.

Seismic Analysis of a Large LNG Tank considering the Effect of Liquid Volume

Large Liquefied Natural Gas (LNG) tanks are prone to damage during strong earthquakes, and accurate seismic analysis must be performed during the design phase to prevent secondary disasters. However, the seismic analysis of large LNG tanks is associated with high computational requirements, which cannot be satisfied by the calculation efficiency of traditional analytical techniques such as the Coupled Eulerian–Lagrangian (CEL) method. Thus, this paper aims to employ a less computationally demanding algorithm, the Smoothed Particle Hydrodynamics-Finite Element Method (SPH-FEM) algorithm, to simulate large LNG tanks. The seismic response of a 160,000 m3 LNG prestressed storage tank is evaluated with different liquid depths using the SPH-FEM algorithm, and simulation results are obtained with excellent efficiency and accuracy. In addition, large von Mises stress at the base of the tank indicates that strong earthquakes can severely jeopardize the structural integrity of large LNG tanks. Therefore, the SPH-FEM algorithm provides a feasible approach for the analysis of large liquid tanks in seismic engineering applications.

Finite element-smoothed particle hydrodynamics adaptive method in simulating debris cloud

The meshless algorithms, especially the smoothed particle hydrodynamics (SPH), are attempted to solve the hypervelocity impact (HVI) problem. However, several limitations of SPH exist in the current studies, such as the tensile instability, the material boundary uncertainty, and the difficulty in defining boundaries. Furthermore, it cannot accurately provide the parameters of the generated fragments. In this paper, we formulate the finite element-smoothed particle hydrodynamics (FEM-SPH) adaptive method to solve the HVI problem by LS-DYNA. It combines the advantages of FEM and SPH by transforming the failed elements into the SPH particles during the simulation. The debris cloud shape is represented by the distribution of the particles in SPH and the exact fragment parameters in FEM, including geometry, temperature, energy, and distribution. By analyzing and optimizing the implementation method, the contact and coupling algorithm, and calculation parameters, we reproduce the experimental results by Piekutowski [39,40] in the numerical simulation. Based on the proposed three typical shapes of the fragments, a systematic statistical analysis is proposed to classify the fragments and analyze their parameters, including speed, momentum, and energy. Risky fragments, i.e., the fragments with large size and high speed, are selected from the overall fragments. We further study the distribution of risky fragments with the details of the evolution in the space and time, which paves the way for further systematic research on the subsequent impact of the debris cloud. Our work shows that the method has a significant and wide application to the debris cloud simulation. The current algorithm can be applied to simulate the Whipple shields with complex structures and advanced material, e.g., sandwich materials, composite materials, foam materials, and gradient materials, or analyze the implosion and fragmentation warhead.

Improvement of surface integrity in the grinding of bioceramic partially stabilized zirconia using analytical, numerical, and experimental methods

In the present paper, the impact of grinding on the surface integrity of the PSZ is investigated through analytical, numerical, and experimental studies. The analytical model of the single grit grinding of the PSZ was developed by taking into consideration the strain rate, the grinding temperature, and the phase transformation of the zirconia. Numerical modeling of the grinding-induced SSD and analysis of the relationship between the parameters of this process and crack formation were performed in the ABAQUS Software via coupled finite element – smoothed particle hydrodynamics (FE-SPH) method. The results showed that, in all cases, the experimental data fall within the ranges calculated via the analytical approach. Moreover, the numerical model revealed that, on average, the numerical results differed from the respective experimental data by less than 15%. Investigation of SEM images of the ground surface indicated more than 17% improvement in the surface integrity together with a reduction in the SSD at 100 μm beneath the ground surface from 3.4% down to 0.9%. The ground surface was further studied using X-ray diffraction (XRD) analysis, with the results indicating the correspondence of the trend of the phase transformation from tetragonal to monoclinic to the increasing trend of the surface integrity and bending strength.