A method for predicting fatigue life of selective laser melting aluminum alloy

Abstract

The application discloses a fatigue life prediction method for selective laser melting aluminum alloy, comprising the following steps: introducing a damage variable to describe material degradation based on the basic concept of continuous damage mechanics, realizing the description of a constitutive equation coupled with damage, and establishing a damage evolution equation considering the additive manufacturing process according to a reference laser volume energy density; obtaining the parameters of the constitutive equation and the damage evolution equation according to the uniaxial tensile test results and the fatigue test data; establishing a numerical calculation method based on the finite element method according to the constitutive equation coupled with damage and the damage evolution equation, realizing the simulation calculation of the fatigue process of the additive manufacturing material, and carrying out the fatigue life prediction of the test piece under different additive manufacturing process parameters. The technical scheme of the application realizes the fatigue damage analysis of the aluminum alloy test piece manufactured by the selective laser melting process considering the additive manufacturing process parameters.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of fatigue damage analysis of additive manufacturing aluminum alloy, and particularly relates to a fatigue life prediction method of selective laser melting aluminum alloy. BACKGROUND

[0002] Additive manufacturing is a new manufacturing technology, which can manufacture complex structural parts that are difficult to obtain by traditional machining methods through a bottom-up construction method. In recent years, additive manufacturing has been increasingly widely applied in the field of aerospace. However, when additive manufacturing metal materials, the laser parameters used will have a great influence on the porosity of the final part, and the defects in the material largely determine the fatigue life of the material. Most of the current damage calculation theoretical models do not fully consider the influence of additive manufacturing process parameters on the fatigue life of the material, and the calculation results differ greatly from the test results. SUMMARY

[0003] The technical problem to be solved by the application is to provide a fatigue life prediction method of selective laser melting aluminum alloy, which adds the influence of additive manufacturing process parameters on the fatigue life of the material to the damage calculation theoretical model, realizes fatigue damage analysis of aluminum alloy test pieces manufactured by selective laser melting process considering additive manufacturing process parameters, and helps fatigue performance analysis of additive manufacturing materials and process route development guidance work.

[0004] To achieve the above-mentioned purpose, the application adopts the following technical solutions:

[0005] A fatigue life prediction method of selective laser melting aluminum alloy, comprising:

[0006] Step S1, based on the basic concept of continuous damage mechanics, a damage variable is introduced to describe the deterioration of the material, a constitutive equation of coupled damage is realized, and a damage evolution equation considering additive manufacturing process is established according to the reference laser volume energy density;

[0007] Step S2, according to the uniaxial tensile test results and fatigue test data, the parameters of the constitutive equation and the damage evolution equation are obtained respectively;

[0008] Step S3, according to the constitutive equation of coupled damage and the damage evolution equation, a numerical calculation method based on the finite element method is established, the simulation calculation of the fatigue process of additive manufacturing materials is realized, and the fatigue life prediction of test pieces under different additive manufacturing process parameters is carried out.

[0009] As a preferred, in step S2, according to the uniaxial tensile test results and fatigue test data, the parameters of the constitutive equation and the damage evolution equation are obtained by least square method or particle swarm optimization algorithm respectively.

[0010] As a preferred, in step S1,

[0011] Damage coupling is performed based on the JC constitutive and strain equivalence assumptions, resulting in the constitutive equation for coupled damage:

[0012] σ=(A+Bε n (1-D)

[0013] Where A, B, and n are constitutive parameters of the material, and D is a one-dimensional damage variable;

[0014] Consider the damage evolution equation for additive manufacturing processes:

[0015]

[0016] Where α, β, m and n are parameters of the material damage evolution equation, and Δ is the energy density influence factor;

[0017] Energy density influence factor Δ:

[0018]

[0019] Where t is a parameter controlling the manufacturing effect of different additive manufacturing parameters, and E d Let E be the volumetric energy density of the laser. The set of process parameters with the longest fatigue test life in the additive manufacturing sample control group is taken as the reference set for the laser volumetric energy density during the analysis, and its volumetric energy density is denoted as E. d0 ;

[0020] Laser volume energy density E d :

[0021]

[0022] Where P is the laser power, v is the laser scanning rate, t is the powder bed thickness, and h is the scanning interval.

[0023] This invention can predict the fatigue life of additively manufactured aluminum alloy specimens under different process parameters with a small number of tests or no tests, reducing repeated tests and calculation costs, while also providing a reference for the formulation of additive manufacturing process routes. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0025] Figure 1This is a flowchart of the fatigue life prediction method for selected area laser melting of aluminum alloy according to an embodiment of the present invention;

[0026] Figure 2 A schematic diagram showing the shape and loading of a smooth test specimen for additive manufacturing materials;

[0027] Figure 3 Peak load-life curves under different stress ratios;

[0028] Figure 4 Damage evolution curves under different additive manufacturing processes. Detailed Implementation

[0029] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0031] Example 1:

[0032] like Figure 1 As shown, this embodiment of the invention provides a method for predicting the fatigue life of selected area laser melting aluminum alloys, including:

[0033] Step S1: Introduce damage variables to describe the material degradation, realize the constitutive equation description of coupled damage, and establish a damage evolution equation considering additive manufacturing process based on the reference laser volume energy density.

[0034] Step S2: Based on the uniaxial tensile test results and fatigue test data, obtain the parameters of the constitutive equation and the damage evolution equation, respectively;

[0035] Step S3: Based on the constitutive equation and damage evolution equation of coupled damage, establish a numerical calculation method based on the finite element method to simulate the fatigue process of additive manufacturing materials and predict the fatigue life of specimens under different additive manufacturing process parameters.

[0036] As one embodiment of the present invention, in step S1, damage mechanics describes the damage in the material by introducing a damage variable. Considering both the rationality of the damage description and the convenience of engineering applications, a one-dimensional damage variable D is introduced into the representative volume element. When D = 1, it signifies complete damage to the material at the representative volume element. Based on the strain equivalence assumption and damage coupling based on the JC constitutive model, the following can be obtained:

[0037] σ=(A+Bε n (1-D)

[0038] Where A, B, and n are constitutive parameters of the material, which can be calibrated using the least squares method or particle swarm optimization algorithm based on data from uniaxial tensile tests.

[0039] Additive manufacturing process parameters include laser power P, laser scanning rate v, powder bed thickness t, and scanning interval h, and the laser volumetric energy density E is defined. d :

[0040]

[0041] Meanwhile, the set of process parameters with the longest fatigue test life in the additive manufacturing sample control group was taken as the reference set for the laser volume energy density during the analysis, and its volume energy density was denoted as E. d0 It is used for subsequent fatigue damage analysis and life prediction calculations.

[0042] Based on the definition of laser bulk energy density above, an energy density influence factor can be further defined to describe the impact of different additive manufacturing parameters on the fatigue properties of the manufactured material, and further reflect the influence of different process parameters on fatigue damage evolution. Considering the ease of application and the effectiveness of the parameter process, the energy density influence factor Δ is defined as follows:

[0043]

[0044] Where t is a parameter that controls the manufacturing effect of different additive manufacturing parameters.

[0045] Based on the energy density influence factor, the existing damage evolution equation can be modified to reflect the impact of different additive manufacturing process parameters on damage evolution. Therefore, a damage evolution equation considering parameterized processes is established:

[0046]

[0047] Here, α, β, m, and n are parameters of the material damage evolution equation, which can be calibrated using the least squares method or particle swarm optimization algorithm based on fatigue experimental data of the material. Combining the constitutive equation of coupled damage and the damage evolution equation, the fatigue life of specimens under different additive manufacturing process parameters can be calculated using the damage mechanics-finite element method.

[0048] In one embodiment of the present invention, in step S2, the least squares method, also known as the least squares method, is a function fitting method that finds the best function match for the data by minimizing the sum of squared errors. Due to its simple principle, fast convergence speed, and ease of understanding and implementation, it is widely used in parameter estimation and is also one of the most common methods for solving curve fitting problems.

[0049] The basic idea of ​​the least squares method is: for a family of curves with M parameters, adjust the M parameters of the model according to N sets of observations (N is greater than M) so as to minimize the sum of squares of the residuals between the observed data and the model predictions. Therefore, the objective function can be defined as the sum of squares of the residuals between the observed data and the model predictions. The least squares method is to find the minimum value of the objective function.

[0050] In the problem of fitting constitutive parameters, the objective function can be taken as:

[0051]

[0052] Where, σ k and ε k All data are observational data. k represents the number of test points taken on the curve (total number N). The minimum value can be obtained by taking the partial derivatives of A, B and n with respect to L1 and setting them equal to zero.

[0053] In the parameter fitting problem of the damage evolution equation, the damage increment equation is first... Integrating from D=0 to D=1, we get:

[0054]

[0055] Therefore, the objective function can be taken as:

[0056]

[0057] Where, N Fk Δ k and σ k All data are observational data. k represents the number of additive manufacturing and fatigue test pieces (total number N). m and n can be obtained by taking the partial derivatives of m and n with respect to L2 and setting them to zero. In smooth parts, α and β are coupled. It is necessary to further use the test results of notched parts and increase their values ​​at equal intervals to carry out numerical calculations to find the most suitable value. In the case of missing notched parts, β = m can be used to simplify the formula. The value can be obtained by taking the partial derivative of α with respect to L2 and setting it to zero.

[0058] Particle Swarm Optimization (PSO) is an optimization model that utilizes information sharing and transmission within a swarm to achieve a globally optimal solution to a problem through the evolution of individual activities within the swarm. Its concept originates from the study of bird flock foraging behavior. The particle swarm represents the swarm, and each particle is an individual. Each particle possesses two important attributes: velocity and position, which are also the two core elements of the PSO algorithm. Furthermore, it is necessary to define the individual's historical best position and the swarm's historical best position to guide individual evolution until the objective function reaches its optimum.

[0059] The evolution of individual activity is described by updating particle velocity and position, with the following update formulas:

[0060]

[0061] Where N is the particle swarm size, i is the particle index, D is the particle dimension, d is the particle dimension index, k is the number of iterations, w is the inertia weight, c1 is the individual learning factor, c2 is the swarm learning factor, and r1 and r2 are random numbers in the interval [0,1] to increase the randomness of the search. Let d be the velocity vector of particle i in the k-th iteration. The position vector of particle i in the d-th dimension during the k-th iteration. The historical optimal position of particle i in the d-th dimension during the k-th iteration is, in other words, the optimal solution obtained by the i-th particle (individual) after the k-th iteration. The historical best position of the swarm in dimension d during the k-th iteration is the optimal solution in the entire swarm after the k-th iteration.

[0062] The velocity update formula can be viewed as consisting of three parts: the first term is the inertia part, which consists of the inertia weight and the individual's own velocity, describing the individual's inertia regarding its previous state of motion; the second term is the cognitive part, which consists of the distance and direction between the individual's current position and its historical best position, describing the individual's reflection on its own experience during the activity; and the third term is the social part, which consists of the distance and direction between the individual's current position and the group's historical best position, describing the influence of other individuals' experiences obtained through information sharing in group activities on the current individual.

[0063] The particle swarm optimization algorithm described above can be used to calibrate the constitutive parameters of the material and the parameters of the damage evolution equation, respectively. The objective functions of the two problems are the same as those of the least squares method, only the solution methods differ. During the calibration process of the particle swarm algorithm, the positions of the particles represent the material parameters to be calibrated, with dimensions representing the number of constitutive parameters and damage evolution equation parameters, respectively. The particle swarm calibration method obtains suitable material parameters by updating the position states of a large number of particles.

[0064] As one embodiment of the present invention, in step S3, the material damage analysis and life prediction method can be implemented with the help of the ABAQUS finite element calculation platform and its subroutine interface. By customizing the damage evolution program and numerically simulating the fatigue process, the fatigue life prediction results of aluminum alloy specimens under specific additive manufacturing process parameters can be obtained.

[0065] A finite element model for numerical simulation is established and appropriately meshed to satisfy the relationship between damage variables and defects in representative volume elements, while applying correct boundary conditions and loads that meet experimental conditions.

[0066] A custom constitutive relation for coupled damage is defined. Based on the information transfer between the ABAQUS finite element calculation platform and the UMAT subroutine, a stress-strain update algorithm for coupled damage is developed to satisfy the aforementioned constitutive model. A damage evolution equation is incorporated to update the damage, thereby updating the material parameters. For linear elastic damage, the damage accumulation within the cycle can be considered linear. Furthermore, it is assumed that the difference in damage accumulation within adjacent N cycles is small. Therefore, the damage increment of the material after N cycles can be obtained, i.e.

[0067]

[0068] Here, the subscripts i and i+1 indicate the number of times the damage is updated. The Young's modulus at the integration point is then updated and used for subsequent stress-strain calculations.

[0069] E i+1 =E(1-D) i+1 )

[0070] Furthermore, step S3 specifically includes:

[0071] (1) Obtain E under various process parameters d By specifying different process parameters such as laser power P, laser scanning rate v, powder bed thickness t, and scanning interval h, specimens manufactured with different process parameters can be obtained.

[0072] (2) After post-treatment of all specimens, uniaxial tensile tests and fatigue tests were performed. The group with the longest fatigue test life was selected as the reference group, and its fatigue life was calculated. Since the internal pores and defects of the specimen are the main cause of fatigue fracture in high-cycle fatigue and ultra-high-cycle fatigue, it can be considered that the parts manufactured under the corresponding parameters with the longest fatigue life have the lowest porosity.

[0073] (3) Fit the constitutive model parameters based on the uniaxial tensile test result curve. This step can be achieved using the least squares method or particle swarm optimization algorithm, i.e., solving for a set of (A,B,n) values ​​to make the objective function... Minimal, where k represents the number of test points taken on the curve.

[0074] (4) Based on the fatigue test results, fit the parameters of the damage evolution equation. This step can be achieved using the least squares method or the particle swarm optimization algorithm, i.e., solving for a set of values ​​(α, β, m, n) such that the objective function... Minimal, where k represents the number of specimens in the fatigue test.

[0075] (5) Calculate E corresponding to each set of process parameters d In ABAQUS software, a smooth finite element model of the specimen is established. Based on the interaction between the ABAQUS platform and subroutines, a user-defined UMAT subroutine is used to perform numerical simulations jointly with ABAQUS. Based on the physical quantities input from ABAQUS to UMAT, the stress and strain at each integration point of each element under cyclic loading are calculated. The damage variable is continuously updated until the damage degree at a certain element integration point reaches 1, at which point the calculation stops, yielding the fatigue life prediction results of the aluminum alloy specimen under specific additive manufacturing process parameters.

[0076] Example:

[0077] The method for fatigue damage analysis of SLM aluminum alloy specimens considering additive manufacturing process parameters described above is explained.

[0078] Assuming there is an existing... Figure 2 The smooth experimental specimen of the additively manufactured material shown was subjected to fatigue tests under fatigue loads with a stress ratio R = -1 / 0.2 / 0.06, and the energy density influence factor composed of additive manufacturing process parameters was quantitatively calculated. Based on the above method, the fatigue damage and life prediction of additively manufactured materials under different processing technologies were analyzed and calculated. Specifically, this includes:

[0079] (1) Conduct multiple fatigue tests under different stress ratios, peak stresses and additive energy density influence factors, and organize the data according to the fatigue test conditions and test results;

[0080] (2) Take the group with the longest fatigue test life and record it as the reference group. At the same time, calculate its fatigue test life. Calculate Δ for each set of process parameters;

[0081] (3) Based on the uniaxial tensile test result curve, the constitutive model parameters of the material are fitted according to the least squares method or particle swarm calibration algorithm: A, B and n;

[0082] (4) Based on the fatigue test life, the parameters of the damage evolution equation are fitted according to the least squares method or the particle swarm calibration algorithm: m, n, α and β;

[0083] (5) In ABAQUS software, a finite element calculation model of the specimen is established to carry out numerical simulation of the fatigue loading process, and the damage variable at the unit integration point is continuously updated with the help of the UMAT subroutine.

[0084] (6) The calculation stops when the damage variable at a certain unit integration point reaches 1, and the fatigue life prediction results of the aluminum alloy specimen under specific additive manufacturing process parameters are obtained.

[0085] Based on the experimental results, fatigue test data were analyzed, and material constitutive and fatigue parameters were calibrated to obtain expressions for load and fatigue life. The peak fatigue load stress and calculated fatigue life values ​​were taken at different stress ratios with an energy density influence factor Δ = 1.0, as shown below. Figure 3 As shown.

[0086] The evolution of damage variables in fatigue simulations under different additive manufacturing processes when the stress ratio R = -1 and the peak stress is 100 MPa is obtained from the extracted results. Figure 4 As shown in the figure, a comparison of the three curves reveals that the introduction of the energy density influence factor Δ makes the damage evolution process related to the material processing process, and simultaneously affects the fatigue life of the material.

[0087] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for predicting the fatigue life of aluminum alloys by selective laser melting, characterized in that, include: Step S1: Based on the basic concepts of continuous damage mechanics, damage variables are introduced to realize the constitutive equation description of coupled damage. Based on the laser volume energy density, a damage evolution equation considering additive manufacturing process is established. Step S2: Based on the uniaxial tensile test results and fatigue test data, obtain the parameters of the constitutive equation and the damage evolution equation, respectively; Step S3: Based on the constitutive equation and damage evolution equation of coupled damage, establish a numerical calculation method based on the finite element method to realize the simulation calculation of the fatigue process of additive manufacturing materials and predict the fatigue life of specimens under different additive manufacturing process parameters. In step S2, based on the results of uniaxial tensile tests and fatigue test data, the parameters of the constitutive equation and damage evolution equation are calibrated using the least squares method or particle swarm optimization algorithm. In step S1, Based on the JC constitutive and strain equivalence assumptions, the constitutive equation for coupled damage is obtained: in, A , B and n For the constitutive parameters of the material, D It is a one-dimensional damage variable; Consider the damage evolution equation for additive manufacturing processes: in, , , m and n 1 is a parameter in the material damage evolution equation, and Δ is the energy density influence factor; Energy density influence factor Δ: in, t Parameters for controlling the manufacturing effect of different additive manufacturing processes. E d Let be the laser volumetric energy density; the set of process parameters with the longest fatigue test life in the additive manufacturing sample control group is taken as the reference set for the laser volumetric energy density during the analysis, and its volumetric energy density is denoted as . E d0 ; Laser volume energy density E d : in, P For laser power, v For laser scanning rate, t 1 For powder bed thickness, h This represents the scan interval.

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