US-20260126359-A1 - METHOD FOR DETERMINING FRACTURE TOUGHNESS OF CEMENTED CARBIDE

US20260126359A1US 20260126359 A1US20260126359 A1US 20260126359A1US-20260126359-A1

Abstract

A method for determining fracture toughness includes: obtaining an elastic modulus, a Poisson's ratio, and a stress-strain curve of a cemented carbide specimen; calculating, based on a fracture calculation formula, a maximum cohesive force; constructing a Mooney-Rivlin model and a cohesive force model in a finite element simulation software to describe characteristics of the cemented carbide specimen; constructing models of the cemented carbide specimen under different fracture modes in the finite element simulation software, and performing J-integral analysis to obtain mode I and mode II fracture energies; and performing a nanoindentation uniaxial compression finite element numerical simulation to obtain simulated values of stress-strain results, performing a nanoindentation experiment on the cemented carbide specimen to obtain experimental values of the stress-strain results, and adjusting parameters in finite element simulation analysis based on differences between the simulated values and the experimental values, and recalculating the mode I and mode II fracture energies.

Inventors

Dan Jia
Wenxuan LI
Haitao Duan
Jian Li
Wulin Zhang
Shengpeng ZHAN
Tian Yang

Assignees

China Academy of Machinery Wuhan Research Institute of Materials Protection Co.,Ltd

Dates

Publication Date: 20260507
Application Date: 20251023
Priority Date: 20241106

Claims (10)

1 . A method for determining fracture toughness of cemented carbide, comprising: preparing a cemented carbide specimen, and performing a tensile mechanical experiment on the cemented carbide specimen to obtain an elastic modulus, a Poisson's ratio, and a stress-strain curve of the cemented carbide specimen; selecting a stress-strain value at a fracture point on the stress-strain curve, and calculating, based on a fracture calculation formula and the stress-strain value, a maximum cohesive force; constructing a Mooney-Rivlin model and a cohesive force model in a finite element simulation software to jointly describe characteristics of the cemented carbide specimen; using, when a crack has not formed in the cemented carbide specimen, the Mooney-Rivlin model as a main constitutive model to describe the characteristics of the cemented carbide specimen; and using, when the crack has formed in the cemented carbide specimen, the cohesive force model as the main constitutive model to describe the characteristics of the cemented carbide specimen; importing the elastic modulus, the Poisson's ratio, and the stress-strain curve into the finite element simulation software, constructing models of the cemented carbide specimen under a plurality of different fracture modes in the finite element simulation software, and performing, based on the models of the cemented carbide specimen, J-integral analysis to obtain a mode I fracture energy and a mode II fracture energy; and importing the mode I fracture energy and the mode II fracture energy into the cohesive force model, performing a nanoindentation uniaxial compression finite element numerical simulation in the finite element simulation software to obtain simulated values of stress-strain results, performing a nanoindentation experiment on the cemented carbide specimen to obtain experimental values of the stress-strain results, and adjusting parameters in finite element simulation analysis based on differences between the simulated values and the experimental values of the stress-strain results, and recalculating the mode I fracture energy and the mode II fracture energy.
2 . The method for determining fracture toughness of cemented carbide as claimed in claim 1 , wherein the calculating, based on a fracture calculation formula and the stress-strain value, a maximum cohesive force comprises: calculating the maximum cohesive force T max using the fracture calculation formula t = ⁢ { K ⁢ δ , δ ⩽ δ c T max , δ > δ c , where t represents a cohesive force, K represents a cohesive force stiffness, δ represents a crack tip opening displacement, and δ c represents a critical displacement; and dividing, during calculation of the maximum cohesive force, the cohesive force into a normal stress value σ and a shear stress value τ through control equations as follows: σ = { σ max δ n 0 ⁢ δ δ ⩽ δ n 0 σ max ⁢ δ n f - δ δ n f - δ n 0 δ > δ n 0 , τ = { τ max δ t 0 ⁢ δ δ ⩽ δ t 0 τ max ⁢ δ t f - δ δ t f - δ t 0 δ > δ t 0 ; where σ max represents a maximum normal stress value, and δ n 0 represents a crack interface opening displacement value corresponding to the maximum normal stress value; τ max represents a maximum shear stress value, and δ t 0 represents a crack interface opening displacement value corresponding to the maximum shear stress value; and δ n f represents a crack interface opening displacement value corresponding to a stress value exceeding σ max , and δ t f represents a crack interface opening displacement value corresponding to a stress value exceeding τ max .
3 . The method for determining fracture toughness of cemented carbide as claimed in claim 1 , wherein the constructing a Mooney-Rivlin model and a cohesive force model in a finite element simulation software to jointly describe characteristics of the cemented carbide specimen comprises: when the crack has not formed in the cemented carbide specimen, using the Mooney-Rivlin model as the main constitutive model for calculating the characteristics of the cemented carbide specimen, and describing a material stress-strain relationship through a strain energy density function: W = C 10 ( I 1 - 3 ) + C 0 ⁢ 1 ( I 2 - 3 ) + 1 d ⁢ ( J - 1 ) 2 ; when the crack has formed in the cemented carbide specimen, using the cohesive force model as the main constitutive model for calculating the characteristics of the cemented carbide specimen, comprising: assuming that there is a cohesive force zone at an interface of the crack or a crack tip of the crack, wherein a material stress-strain relationship in the cohesive force zone is different from that in other regions; defining a constitutive relationship and a damage evolution law of the cohesive force zone; and simulating debonding of the interface and propagation of the crack.
4 . The method for determining fracture toughness of cemented carbide as claimed in claim 1 , wherein the importing the elastic modulus, the Poisson's ratio, and the stress-strain curve into the finite element simulation software, constructing models of the cemented carbide specimen under a plurality of different fracture modes in the finite element simulation software, and performing, based on the models of the cemented carbide specimen, J-integral analysis to obtain a mode I fracture energy and a mode II fracture energy comprises: constructing, based on linear elastic fracture mechanics, micro-pillar models of the cemented carbide specimen for an opening mode, a sliding mode and a tearing mode, and calculating stress-strain results for opening-mode fracture, in-plane shear fracture, and transverse shear fracture by using the micro-pillar models, respectively; determining, according to the stress-strain results for the opening-mode fracture, the in-plane shear fracture and the transverse shear fracture, stress angular variations for the micro-pillar models of the cemented carbide specimen for the opening mode, the sliding mode and the tearing mode; importing the stress angular variations for the micro-pillar models of the cemented carbide specimen for the opening mode, the sliding mode and the tearing mode into a partial derivative equation of crack tip asymptotic solution to obtain a relationship among stress, angle and a distance from an integration point to a crack tip of the crack; and performing, based on the relationship among the stress, the angle and the distance from the integration point to the crack tip, the J-integral analysis to obtain the mode I fracture energy and the mode II fracture energy.
5 . The method for determining fracture toughness of cemented carbide as claimed in claim 1 , wherein the performing a nanoindentation uniaxial compression finite element numerical simulation in the finite element simulation software to obtain simulated values of stress-strain results, performing a nanoindentation experiment on the cemented carbide specimen to obtain experimental values of the stress-strain results, and adjusting parameters in finite element simulation based on differences between the simulated values and the experimental values of the stress-strain results, and recalculating the mode I fracture energy and the mode II fracture energy comprises: importing the mode I fracture energy and the mode II fracture energy into the cohesive force model in the finite element simulation software; performing the nanoindentation uniaxial compression finite element numerical simulation in the finite element simulation software on the models of the cemented carbide specimen to obtain the simulated values of the stress-strain results, performing the nanoindentation experiment on the cemented carbide specimen to obtain the experimental values of the stress-strain results, and adjusting, based on magnitudes of the simulated values and the experimental values of the stress-strain results, a mesh size and a mesh number in the finite element simulation software; performing the nanoindentation uniaxial compression finite element numerical simulation in the finite element simulation software on the models of the cemented carbide specimen under different pressure conditions to obtain simulated values under different pressure conditions, performing the nanoindentation experiment on the cemented carbide specimen to obtain the experimental values of the stress-strain results, and adjusting uncertain parameters in the finite element simulation analysis based on differences between the simulated values under different pressure conditions and the experimental values of the stress-strain results; and recalculating the mode I fracture energy and the mode II fracture energy.
6 . The method for determining fracture toughness of cemented carbide as claimed in claim 5 , wherein the performing the nanoindentation uniaxial compression finite element numerical simulation in the finite element simulation software on the models of the cemented carbide specimen to obtain the simulated values of the stress-strain results, performing the nanoindentation experiment on the cemented carbide specimen to obtain the experimental values of the stress-strain results, and adjusting, based on magnitudes of the simulated values and the experimental values of the stress-strain results, a mesh size and a mesh number in the finite element simulation software comprises: reducing the mesh size and decreasing the number of meshes when computation time is too long; refining a mesh in a fracture part, reducing the mesh size and increasing the mesh number when accuracy of simulation results is low.
7 . The method for determining fracture toughness of cemented carbide as claimed in claim 5 , wherein the performing the nanoindentation uniaxial compression finite element numerical simulation in the finite element simulation software on the models of the cemented carbide specimen under different pressure conditions to obtain simulated values under different pressure conditions, performing the nanoindentation experiment on the cemented carbide specimen to obtain the experimental values of the stress-strain results, and adjusting uncertain parameters in the finite element simulation based on differences between the simulated values under different pressure conditions and the experimental values of the stress-strain results comprises: performing, when an error between the simulated values under different pressure conditions and the experimental values of the stress-strain results exceeds a threshold, uncertainty parameter impact analysis on the uncertain parameters in the finite element simulation to assess impact weights of the uncertain parameters on calculation results of the fracture toughness, wherein the uncertain parameters comprise material parameters of the cemented carbide specimen, geometric parameters of the cemented carbide specimen, and loading conditions in the finite element simulation software; and adjusting, based on results of the uncertainty parameter impact analysis, the uncertain parameters.
8 . The method for determining fracture toughness of cemented carbide as claimed in claim 6 , wherein the performing the nanoindentation uniaxial compression finite element numerical simulation in the finite element simulation software on the models of the cemented carbide specimen under different pressure conditions to obtain simulated values under different pressure conditions comprises: performing the nanoindentation uniaxial compression finite element numerical simulation with multiple pressure values incremented by 20 millinewtons (mN).
9 . The method for determining fracture toughness of cemented carbide as claimed in claim 8 , wherein the multiple pressure values incremented by 20 mN are 50 mN, 70 mN, 90 mN, 110 mN, 130 mN, 150 mN, 170 mN, 190 mN, and 210 mN.
10 . The method for determining fracture toughness of cemented carbide as claimed in claim 1 , wherein a mesh size used in finite element simulation is less than a size threshold, and the size threshold ranges from 0.3 to 0.7 micrometers (μm).

Description

CROSS-REFERENCE TO RELATED APPLICATION This application claims priority to Chinese Patent Application No. 202411573041.X, filed Nov. 6, 2024, which is herein incorporated by reference in its entirety. TECHNICAL FIELD The disclosure relates to the field of cemented carbide (also referred to as hard alloy) performance testing, and more particularly to a method for determining fracture toughness of cemented carbide. BACKGROUND In recent years, physical vapor deposited (PVD) cemented carbide coatings have shown great potential in improving surface properties and extending the service life of metal components due to their excellent thermal stability, mechanical properties, oxidation resistance, and corrosion resistance. However, the insufficient toughness of the cemented carbide coatings can lead to brittle spalling during friction, causing gradual wear and failure of metal components. The lack of strength and toughness severely limits the application of the cemented carbide coatings in extreme conditions such as marine, nuclear, and aerospace environments Fracture toughness, as one of the main mechanical properties of cemented carbide materials, is an index that measures ability of a material to resist crack propagation in the presence of cracks or similar defects. This ability can be described by parameters such as energy release rate, stress intensity factor, crack tip opening displacement (CTOD), and J-integral. Materials with high fracture toughness can prevent or delay crack propagation when cracks occur, thereby enhancing the safety and reliability of structures. This is crucial for ensuring the safe operation of important engineering structures. Currently, the fracture toughness is generally measured through experiments. However, conventional fracture toughness testing involves complex steps, including sample preparation, fixture selection, displacement gauge connection, load application, crack size measurement, and fracture toughness calculation. Moreover, the test results are influenced by various factors such as cross-sectional dimensions, temperature, and strain rate. Using the finite element method to determine the fracture toughness of cemented carbide coatings, relevant nanoindentation simulations have already established numerical models. However, conventional simulation can only calculate the elastic properties of the film, such as hardness and elastic modulus, from the load-displacement curve, and cannot provide information on the film performance, making it difficult to reasonably determine the fracture toughness parameters of the cemented carbide. Therefore, there are still significant issues in the fracture simulation of cemented carbide coatings. SUMMARY The disclosure provides a method for determining fracture toughness of cemented carbide, including: preparing a cemented carbide specimen, and performing a tensile mechanical experiment on the cemented carbide specimen to obtain an elastic modulus, a Poisson's ratio, and a stress-strain curve of the cemented carbide specimen;selecting a stress-strain value at a fracture point on the stress-strain curve, and calculating, based on a fracture calculation formula and the stress-strain value, a maximum cohesive force;constructing a Mooney-Rivlin model and a cohesive force model in a finite element simulation software to jointly describe characteristics of the cemented carbide specimen; using, when a crack has not formed in the cemented carbide specimen, the Mooney-Rivlin model as a main constitutive model to describe the characteristics of the cemented carbide specimen; and using, when the crack has formed in the cemented carbide specimen, the cohesive force model as the main constitutive model to describe the characteristics of the cemented carbide specimen;importing the elastic modulus, the Poisson's ratio, and the stress-strain curve into the finite element simulation software, constructing models of the cemented carbide specimen under multiple different fracture modes in the finite element simulation software, and performing, based on the models of the cemented carbide specimen, J-integral analysis to obtain a mode I fracture energy and a mode II fracture energy; andimporting the mode I fracture energy and the mode II fracture energy into the cohesive force model, performing a nanoindentation uniaxial compression finite element numerical simulation in the finite element simulation software to obtain simulated values of stress-strain results, performing a nanoindentation experiment on the cemented carbide specimen to obtain experimental values of the stress-strain results, and adjusting parameters in finite element simulation analysis based on differences between the simulated values and the experimental values of the stress-strain results, and recalculating the mode I fracture energy and the mode II fracture energy. In an embodiment, the method further includes: determining, based on the mode I fracture energy and the mode II fracture energy