Method for obtaining constitutive relation and fracture performance of complex thin-walled die casting at any position

Abstract

The present application relates to the field of predicting the constitutive and fracture performance of thin-walled die-cast aluminum parts from FLOW3D simulation results, and discloses a method for obtaining the constitutive and fracture performance of a complex thin-walled die-cast part at any position, comprising the following steps: Step one, performing mold flow simulation on the target part, and the mold flow simulation results include the solidification time and porosity at any position of the training part; Step two, inputting the solidification time and porosity at any position of the target part into a multilayer perceptron model, and the multilayer perceptron model outputs the mechanical parameters of the target part at any position, including the hardening curve scaling factor and the fracture surface scaling factor. Step three, preparing a flat plate mold with the same material as the target part, performing basic mechanical property testing on the flat plate mold, and obtaining the reference mechanical properties.

Description

Technical Field

[0001] This invention relates to the field of predicting the constitutive and fracture properties of thin-walled die-cast aluminum parts from mold flow simulation results, and specifically to a method for obtaining the constitutive and fracture properties of complex thin-walled die-cast parts at arbitrary locations. Background Technology

[0002] Traditional collision simulations often assume complex parts are made of a single homogeneous material, assigning uniform material properties. This simplification differs significantly from actual working conditions, leading to large errors in simulation results. In actual die casting, differences in filling flow, cooling rate, and local solidification behavior often result in casting defects such as porosity and shrinkage, causing significant spatial heterogeneity in mechanical properties—different regions exhibiting different strength, plasticity, and fracture characteristics. Ignoring this non-uniformity in property distribution during the design phase will lead to large discrepancies between simulation results and measured data, severely impacting the accuracy of component reliability assessment and lightweight design. To improve simulation accuracy, this spatial distribution of properties must be considered. This study innovatively introduces an automatic partitioning algorithm, dividing the original input mesh into multiple sub-regions based on the part's geometric features and potential performance gradients. Each sub-region is assigned different material properties, thereby improving prediction accuracy.

[0003] The core challenge lies in obtaining the true mechanical properties corresponding to these zones. While local sampling tests can directly obtain material parameters, for die castings with complex thin-walled and multi-ribbed structures, the number and locations of representative samples are limited, making it difficult to fully characterize the performance distribution across the entire part. Therefore, a method for obtaining constitutive and fracture properties at arbitrary locations in complex thin-walled die castings is needed. This method should be able to accurately infer the full-field mechanical properties of die castings based on limited experimental data, providing crucial data support for performance-driven design of die castings. Summary of the Invention

[0004] The present invention aims to provide a method for obtaining the constitutive and fracture properties of complex thin-walled die-cast parts at any position. Its core lies in an MLP machine learning method that predicts the constitutive and fracture properties of thin-walled die-cast aluminum parts based on mold flow simulation results.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a method for obtaining constitutive and fracture properties of complex thin-walled die-cast parts at arbitrary positions, comprising the following steps:

[0006] Step 1: Perform mold flow simulation on the target part. The mold flow simulation results include the solidification time and porosity at any position of the training part.

[0007] Step 2: Input the solidification time and porosity of any position of the target part into the multilayer perceptron model. The multilayer perceptron model outputs the mechanical parameters of any position of the target part, including the hardening curve scaling factor and the fracture surface scaling factor.

[0008] Step 3: Prepare a flat plate mold made of the same material as the target part. Perform basic mechanical property tests on the flat plate mold to obtain reference mechanical properties, which include a reference constitutive curve and a reference fracture surface. Scale the reference constitutive curve according to the scaling factor of the hardening curve to obtain the constitutive properties at any location. Scale the reference fracture surface according to the scaling factor of the fracture surface to obtain the fracture properties at any location.

[0009] The beneficial effects of this plan are:

[0010] Based on a multilayer perceptron model, a functional relationship between solidification time, porosity, and mechanical parameters at different locations is constructed. Due to the continuous nature of the data from mold flow simulation, the multilayer perceptron model can output mechanical parameters at any location. In this invention, the mechanical parameters are the hardening curve scaling factor and the fracture surface scaling factor. Specifically, the constitutive properties at any location are obtained by multiplying the reference constitutive curve and the hardening curve scaling factor, and the fracture properties at any location are obtained by multiplying the reference fracture surface and the fracture surface scaling factor. This method obtains the material constitutive relationship and fracture parameters at any location of the die casting, ensuring both data accuracy and continuity. Furthermore, the training method of the multilayer perceptron model is as follows:

[0011] Step 2.1: Perform mold flow simulation on the training parts. The mold flow simulation results include solidification time and porosity.

[0012] Step 2.2: Prepare and train a flat mold with the same material as the parts, and conduct basic mechanical property tests on the flat mold to obtain reference mechanical properties;

[0013] Step 2.3: Take samples of three-point bending specimens at different positions on the training part, perform three-point bending tests on the three-point bending specimens, and obtain the measured mechanical properties.

[0014] Step 2.4: Input the reference mechanical properties into the material card, and simulate the three-point bend specimen based on the material card. The material card parameters include the hardening curve shrinkage factor and the fracture surface shrinkage factor. Adjust the hardening curve shrinkage factor and the fracture surface shrinkage factor to align the measured mechanical properties with the reference mechanical properties and obtain the adjusted hardening curve shrinkage factor and fracture surface shrinkage factor.

[0015] Step 2.5: Train the multilayer perceptron model, using the simulation results as input features and the scaling factors of the hardening curve and the fracture surface at different locations as target variables.

[0016] Furthermore, the material card parameters also include Young's modulus.

[0017] Furthermore, in step 2.2, a flat plate mold is used as a sampling carrier to obtain standard specimens for uniaxial tension, notch, shear, and cupping tests, and the basic mechanical properties of the standard specimens are tested.

[0018] Furthermore, in step 2.2, the reference mechanical properties include the reference hardening curve. Dimensionless strain rate ε * Stress triaxiality η, material strain rate sensitivity coefficient D4, and material failure parameters D1, D2, and D3;

[0019] In step 2.3, the measured mechanical properties include the measured hardening curve. and fracture surface strain ;

[0020] Step 2.4 specifically includes the following steps:

[0021] Step 2.4.1: Perform solid modeling on all samples, input the reference mechanical properties into the material card, simulate the solid model based on the material card, and adjust the scaling factor of the hardening curve and the scaling factor of the fracture surface to align the measured mechanical properties with the reference mechanical properties.

[0022] Hardening curve scaling factor satisfy:

[0023] (The formula for obtaining the constitutive properties (measured hardening curve) at any position by scaling the constitutive curve according to the scaling factor of the hardening curve is as follows:)

[0024] Fracture surface scaling factor satisfy:

[0025] (The formula for the fracture performance (fracture surface strain) at any location is obtained by scaling the fracture surface root using the scaling factor.)

[0026] 2.4.2 Shell modeling is performed on specimens with a thickness less than the design thickness. The shell model is simulated based on the hardening curve scaling factor and fracture surface scaling factor obtained in step 2.4.1. The material card parameters also include the hardening curve scaling factor and the fracture surface scaling factor of the shell model. The material card parameters are then adjusted a second time based on the following formula:

[0027] ;

[0028] ;

[0029] λ1 and λ2 are both second-order correction coefficients;

[0030] The adjusted hardening curve scaling factor and fracture surface scaling factor are used as mechanical parameters for the training part at locations where the thickness is less than the design thickness.

[0031] Furthermore, in step 2.3, samples of different thicknesses are selected for testing by sampling method; in step 2.4.2, after obtaining the material card parameters of samples of different thicknesses, the material card parameters of the shell model of the intermediate thickness sample are derived by interpolation method.

[0032] Furthermore, in step 2.5, before machine learning, the scaling factor of the hardening curve and the scaling factor of the fracture surface are normalized.

[0033] This solution also has the following effects:

[0034] 1. The process parameters of each part in the mold flow simulation are continuous and complete, but the accuracy is not high and there are defects because the entire process is calculated by machine and there is a lack of measured data. While the mechanical parameters of different parts of the part can be obtained by actual measurement, the number of samples is insufficient for thin-walled, multi-ribbed or die-cast parts with internal features, resulting in discontinuous data.

[0035] Therefore, this multilayer perceptron model constructs a functional relationship between defect data and mechanical parameters at different locations, thereby enabling the prediction of constitutive and fracture at any location.

[0036] 2. Due to the difficulty in obtaining standard specimens from parts using conventional methods, this approach involves machining specimens on a flat mold made of the same material as the part to obtain the specimens required for basic mechanical property testing. Reference material cards are then obtained through simulation calculations to initially address the sampling difficulty. While the simulation results include mechanical property information at various locations, the data accuracy is not high. The test results for the specimens are accurate, but the number of specimens is insufficient. Therefore, by benchmarking the two sets of data, the parameters of the material card are adjusted. These adjusted parameters are then used for machine learning, employing a multilayer perceptron model to predict the mechanical properties at all locations on the part, thus solving the problem of blind spots in the inspection of complex parts.

[0037] 3. Since shell elements cannot accurately represent the evolution of strain and cumulative damage along the thickness direction, the theoretical assumptions of shell modeling in the simulation of three-point bending of thick plates differ greatly from the actual situation. Therefore, the prediction results of solid model are more accurate than those of shell model.

[0038] However, some areas are thinner, making shell modeling more efficient. Therefore, a hybrid modeling approach is used for the overall part. For these thinner areas, solid modeling is performed first for parameter adjustment, followed by shell modeling. Based on the results of the first adjustment, a second parameter adjustment is made to ensure the efficiency of subsequent mechanical learning. In this invention, "design thickness" refers to the thickness of the three-point bend specimen (less than the design thickness), which requires shell modeling; typically, the design thickness is 4mm.

[0039] After obtaining the material card parameters for samples of different thicknesses, the material card parameters for the shell model of the intermediate thickness sample are derived using interpolation. This setup allows for the acquisition of more mechanical property information for samples of different thicknesses through the difference method, thereby improving the training effect. In this invention, "intermediate thickness" refers to the thickness between any two sample thickness values ​​in step two. Before training the multilayer perceptron model, the scaling factors of the hardening curve and the fracture surface need to be normalized. Specifically, the constitutive scaling factor and the fracture scaling factor are processed according to certain rules to ensure they fall into the (0,1) range as decimals, thus eliminating the influence of different dimensions on the final result. (See attached figures.)

[0040] Figure 1 This is a flowchart of Example 1;

[0041] Figure 2 This is a schematic diagram showing the range of influence of the material card parameters on the hardening curve in Example 1;

[0042] Figure 3 This is a sample image of the three-point bend test specimen on the front of the part in Example 1;

[0043] Figure 4 This is a sample image of the three-point bend specimen on the reverse and side surfaces of the part in Example 1;

[0044] Figure 5 This is the design drawing for the flat plate mold sampling of Example 1. Detailed Implementation

[0045] The following detailed description illustrates the specific implementation method:

[0046] Example 1

[0047] Example 1 is basically as follows Figure 1 As shown: A method for obtaining constitutive and fracture properties of complex thin-walled die-cast parts at arbitrary locations, comprising the following steps:

[0048] Step 1: Perform mold flow simulation on the target part. The mold flow simulation results include the solidification time and porosity at any position of the training part.

[0049] Step 2: Input the solidification time and porosity of any position of the target part into the multilayer perceptron model. The multilayer perceptron model outputs the mechanical parameters of any position of the target part, including the hardening curve scaling factor and the fracture surface scaling factor.

[0050] Step 3: Prepare a flat mold made of the same material as the target part. Perform basic mechanical property tests on the flat mold to obtain reference mechanical properties, including a reference constitutive curve and a reference fracture surface. Scale the reference constitutive curve according to the hardening curve scaling factor to obtain the constitutive properties at any location. Scale the reference fracture surface according to the root fracture surface scaling factor to obtain the fracture properties at any location.

[0051] The training method for the multilayer perceptron model is as follows:

[0052] Step 2.1: Perform mold flow simulation on the training parts. The mold flow simulation results include solidification time and porosity.

[0053] Step 2.2: Prepare a flat mold made of the same material as the training parts. The method for making the flat mold is as follows: when producing the training parts, use the same process to die-cast a homogeneous flat mold.

[0054] Using a flat mold as a sampling carrier, standard specimens for uniaxial tension, notch, shear, and cupping tests are obtained. The standard specimens are as follows: Figure 5 As shown, basic mechanical property tests were performed on the standard specimen to obtain reference mechanical properties, which include a reference constitutive curve and a reference fracture surface. The reference constitutive curve includes a reference hardening curve. Dimensionless strain rate ε * Stress triaxiality η, material strain rate sensitivity coefficient D4, and material failure parameters D1, D2, and D3;

[0055] The Johnson-Cook model is an empirical failure model widely used for metallic materials and certain polymers under large deformation and high strain rate scenarios such as high-speed impact, explosion, and cutting. It describes how the failure strain of a material (i.e., the strain at which the material begins to fracture) is affected by stress state, strain rate, and temperature.

[0056] These three parameters, D1, D2, and D3, are the core failure parameters of this model. Together, they determine the dependence of the failure strain of the material on the stress triaxiality under quasi-static, room temperature conditions.

[0057] The specific definitions of the three parameters are as follows:

[0058] D1: An approximate failure strain under pure shear (zero-stress triaxiality); D1 can be regarded as the toughness benchmark of a material under shear-dominated failure modes (such as perforation and shearing). It is a fitting parameter, but its value is close to the failure strain measured in a pure shear test.

[0059] D2: The attenuation coefficient of failure strain under high stress triaxiality; the larger the D2, the greater the attenuation of failure strain relative to the shear state (D1) under high stress triaxiality.

[0060] D3: Controls the sensitivity of failure strain to stress triaxiality; D3 determines the "steepness" of the failure strain curve as stress triaxiality changes. The larger the absolute value of D3, the steeper the curve drops, meaning that the material is more "sensitive" to stress triaxiality.

[0061] D2 and D3 work together to describe the change in failure strain with triaxiality. D2 and D3 are strongly coupled and cannot be understood separately. Together, they fit the shape of the curve of failure strain as a function of triaxiality.

[0062] The hardening curve is a curve that describes the relationship between flow stress and deformation during plastic deformation of a material;

[0063] Dimensionless strain rate is usually defined as the ratio of the current strain rate to the reference strain rate;

[0064] Stress triaxiality is defined as the ratio of mean stress to equivalent stress, and is a key indicator for measuring whether the stress state is "tension" or "compression".

[0065] Material failure parameters and material strain rate sensitivity coefficients are constants that need to be determined through a series of mechanical experiments (such as tensile tests and shear tests with different notch radii).

[0066] Step 2.3: Take three-point bend samples at different locations on the training part, such as... Figure 3 , Figure 4 As shown, the blue area indicates the sampling location. The cross-sectional dimensions of the three-point bend specimens are uniformly 40mm × 30mm, and the thickness is adjusted according to the sampling location. The span during testing is set to 30mm. Three-point bend tests are performed on the specimens to obtain the measured mechanical properties, including the measured hardening curve. and fracture surface strain ;

[0067] Step 2.4: Perform data cleaning and analysis on the mechanical parameters, solidification time and porosity obtained in steps 2.1-2.4. Data cleaning involves analyzing the expected value and standard deviation of the original data, and then removing data outside the distribution band formed by the expected value and standard deviation.

[0068] The data analysis assumes that the data follows a normal distribution, meaning that the values ​​of the ordinates under the same x-axis follow a normal distribution. A smoothing window normal distribution probability weighting method is proposed. Specifically, the data is divided into several equal intervals according to the x-axis range. At the midpoint of each interval, the expected value and variance of all data points within that interval are calculated. Using the normal distribution assumption, the probability of each data point is calculated. The probabilities of all data points within the interval are normalized into weights, and the final weighted value is output. This analytical method, through probability weighting, eliminates the interference of data randomness and provides an intuitive predictive trend for the influence of solidification time and porosity on the constitutive shrinkage factor.

[0069] The reference mechanical properties are input into the material card, and the three-point bend specimen is simulated based on the material card. The parameters of the material card are adjusted to align the measured mechanical properties with the reference mechanical properties.

[0070] Specifically, the following steps are included:

[0071] 2.4.1 Solid modeling was performed on all three-point bend specimens. The reference mechanical properties were input into the material card. The solid model was simulated based on the material card. The parameters of the material card were adjusted to align the measured mechanical properties with the reference mechanical properties.

[0072] The material card parameters include Young's modulus, hardening curve shrinkage factor, and fracture surface shrinkage factor. Young's modulus is a physical quantity that describes the ability of a solid material to resist deformation, and is defined as the ratio of stress to strain.

[0073] like Figure 2 As shown, the measured hardening curve obtained from the three-point bending test can be divided into four stages: elastic deformation stage, yielding stage, uniform plastic deformation stage, and necking stage. To improve simulation benchmarking efficiency, three parameters were selected for material card parameter benchmarking: Young's modulus (controlling the elastic deformation stage), hardening curve scaling factor (regulating plastic deformation behavior), and fracture surface scaling factor (determining fracture characteristics), corresponding to... Figure 2 The three areas are divided by the red dotted line.

[0074] Hardening curve scaling factor Satisfies (based on MAT24 material card):

[0075] ;

[0076] Fracture surface scaling factor Satisfies (based on JC principles):

[0077] ;

[0078] 2.4.2 Shell modeling is performed on the three-point bend specimen with a thickness less than the design thickness. The shell model is simulated based on the material card parameters obtained in step 2.4.1. The material card parameters also include the scaling factor of the shell model hardening curve and the scaling factor of the shell model fracture surface. The material card parameters are adjusted a second time based on the following formula:

[0079] ;

[0080] ;

[0081] λ1 and λ2 are both second-order correction coefficients;

[0082] The adjusted hardening curve scaling factor and fracture surface scaling factor are used as mechanical parameters for the training part at locations where the thickness is less than the design thickness.

[0083] Step 2.5: Normalize the scaling factors of the hardening curve and the fracture surface. Train a multilayer perceptron (MLP) model. The input features of the MLP model are the solidification time and porosity from Step 1, and the target variables are Young's modulus, the scaling factor of the hardening curve, and the scaling factor of the fracture surface.

[0084] The multilayer perceptron model includes a preprocessing module, a model training module, and a data prediction module.

[0085] The preprocessing module uses Pandas functions to read data, handle missing values, and remove outliers from the solidification time and porosity datasets of the training parts.

[0086] The model training module uses the random forest regression algorithm for learning and a nested 10-fold cross-validation method for training data.

[0087] The data prediction module combines the mean absolute error (MAE) and the mean absolute percentage error (MAPE) to evaluate the accuracy and generalization ability of the model predictions. The calculation formula is as follows:

[0088] ;

[0089] ;

[0090] Represents experimental values. m represents the predicted value, and m represents the number of experimental values.

[0091] The lower the MAPE value, the better the prediction performance; the closer the MAE value is to 0, the more accurate the model prediction.

[0092] Example 2

[0093] Based on Example 1: In step 2.3, samples of different thicknesses are selected for testing by sampling method; in step 2.4.2, after obtaining the material card parameters of samples of different thicknesses, the material card parameters of the shell model of the intermediate thickness sample are derived by interpolation method.

[0094] The above descriptions are merely embodiments of the present invention, and common knowledge such as specific technical solutions and / or characteristics are not described in detail here. It should be noted that those skilled in the art can make various modifications and improvements without departing from the technical solutions of the present invention, and these should also be considered within the scope of protection of the present invention. These modifications and improvements will not affect the effectiveness of the implementation of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A method for obtaining constitutive and fracture properties of complex thin-walled die-cast parts at arbitrary locations, characterized in that, Includes the following steps: Step 1: Perform mold flow simulation on the target part. The mold flow simulation results include the solidification time and porosity at any position of the training part. Step 2: Input the solidification time and porosity of any position of the target part into the multilayer perceptron model. The multilayer perceptron model outputs the mechanical parameters of any position of the target part, including the hardening curve scaling factor and the fracture surface scaling factor. Step 3: Prepare a flat mold made of the same material as the target part. Perform basic mechanical property tests on the flat mold to obtain reference mechanical properties. The reference mechanical properties include the reference constitutive curve and the reference fracture surface. Multiply the reference constitutive curve and the hardening curve by the scaling factor to obtain the constitutive properties at any position. Multiply the reference fracture surface and the fracture surface by the scaling factor to obtain the fracture properties at any position.

2. The method for obtaining constitutive and fracture properties of complex thin-walled die-cast parts at arbitrary positions according to claim 1, characterized in that, The training method for the multilayer perceptron model is as follows: Step 2.1: Perform mold flow simulation on the training parts. The mold flow simulation results include solidification time and porosity. Step 2.2: Prepare and train a flat mold with the same material as the parts, and conduct basic mechanical property tests on the flat mold to obtain reference mechanical properties; Step 2.3: Take samples of three-point bending specimens at different positions on the training part, perform three-point bending tests on the three-point bending specimens, and obtain the measured mechanical properties. Step 2.4: Input the reference mechanical properties into the material card, and simulate the three-point bend specimen based on the material card. The material card parameters include the hardening curve shrinkage factor and the fracture surface shrinkage factor. Adjust the hardening curve shrinkage factor and the fracture surface shrinkage factor to align the measured mechanical properties with the reference mechanical properties and obtain the adjusted hardening curve shrinkage factor and fracture surface shrinkage factor. Step 2.5: Train the multilayer perceptron model, using the simulation results as input features and the scaling factors of the hardening curve and the fracture surface at different locations as target variables.

3. The method for obtaining constitutive and fracture properties of complex thin-walled die-cast parts at arbitrary positions according to claim 2, characterized in that: The material card parameters also include Young's modulus.

4. The method for obtaining constitutive and fracture properties of complex thin-walled die-cast parts at arbitrary positions according to claim 2, characterized in that: In step 2.2, a flat plate mold is used as a sampling carrier to obtain standard specimens for uniaxial tension, notch, shear, and cupping tests, and the basic mechanical properties of the standard specimens are tested.

5. The method for obtaining constitutive and fracture properties of a complex thin-walled die-casting part at any position according to claim 2, characterized in that: In step 2.2, the reference mechanical properties include the reference hardening curve. Dimensionless strain rate ε * Stress triaxiality η, material strain rate sensitivity coefficient D4, and material failure parameters D1, D2, and D3; In step 2.3, the measured mechanical properties include the measured hardening curve. and fracture surface strain ; Step 2.4 specifically includes the following steps: Step 2.4.1: Perform solid modeling on all samples, input the reference mechanical properties into the material card, simulate the solid model based on the material card, and adjust the scaling factor of the hardening curve and the scaling factor of the fracture surface to align the measured mechanical properties with the reference mechanical properties. Hardening curve scaling factor satisfy: ； Fracture surface scaling factor satisfy: ； 2.4.2 Shell modeling is performed on specimens with a thickness less than the design thickness. The shell model is simulated based on the hardening curve scaling factor and fracture surface scaling factor obtained in step 2.4.

1. The material card parameters also include the hardening curve scaling factor and the fracture surface scaling factor of the shell model. The material card parameters are then adjusted a second time based on the following formula: ； ； λ1 and λ2 are both second-order correction coefficients; The adjusted hardening curve scaling factor and fracture surface scaling factor are used as mechanical parameters for the training part at locations where the thickness is less than the design thickness.

6. The method for obtaining constitutive and fracture properties of a complex thin-walled die-casting part at any position according to claim 5, characterized in that: In step 2.3, samples of different thicknesses are selected for testing using a sampling method; in step 2.4.2, after obtaining the material card parameters of samples of different thicknesses, the material card parameters of the shell model of the intermediate thickness sample are derived using an interpolation method.

7. The method for obtaining constitutive and fracture properties of complex thin-walled die-cast parts at arbitrary positions according to claim 1, characterized in that: In step 2.5, before machine learning, the scaling factor of the hardening curve and the scaling factor of the fracture surface are normalized.

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