A failure prediction method for isotropic materials
By constructing a failure function based on Mohr's theory and utilizing tensile and compressive strength parameters, the accuracy problem of failure criteria for isotropic materials under complex stress states was solved, achieving high-precision failure prediction and analytical prediction of shear strength, applicable to a variety of materials.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA AIRPLANT STRENGTH RES INST
- Filing Date
- 2026-05-25
- Publication Date
- 2026-06-19
AI Technical Summary
Existing failure criteria for isotropic materials have low prediction accuracy under complex stress states, rely on empirical parameters, and have inconsistent expressions, making it difficult to meet the needs of engineering applications.
A failure function based on Mohr's theory is constructed using two fundamental parameters: tensile strength and compressive strength. Undetermined coefficients are determined by the assumptions of hydrostatic loading and uniaxial loading. The failure envelope and fracture surface angle under complex stress states are predicted, and the shear strength is analytically predicted.
It achieves high-precision prediction of failure under complex stress states, reduces test costs and parameter requirements, is applicable to a variety of materials, including thermosetting resins, thermoplastic resins and metals, and provides simple and highly analytical prediction results, making it suitable for engineering applications.
Smart Images
Figure CN122245570A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of strength prediction technology for isotropic materials, specifically to a failure prediction method applicable to isotropic materials, particularly applicable to failure prediction of isotropic materials such as resin matrices (including thermosetting resins and thermoplastic resins) and metals under complex stress states. Background Technology
[0002] Carbon fiber reinforced resin matrix composites are widely used in the aerospace field due to their excellent properties of being lightweight and having high strength. Many researchers employ micromechanical analysis methods to study the mechanical behavior of thermosetting / thermoplastic composites. In representative volume elements, the fibers and matrix are considered isotropic materials; therefore, the accuracy of predicting the mechanical behavior of the component materials strongly depends on isotropic material strength theory, the core of which lies in isotropic material failure criteria.
[0003] Since the establishment of classical mechanics, the study of failure criteria for isotropic materials has attracted widespread attention from academia and industry. The Mohr-Coulomb criterion, as a classical strength theory, can describe the failure behavior of materials under combined compressive and shear stresses, but its prediction error for the uniaxial tensile fracture surface angle of materials such as cast iron is relatively large. Furthermore, existing modifications to the Mohr-Coulomb criterion either rely on fitting large amounts of experimental data or are complex in form, making them inconvenient for engineering applications.
[0004] Despite extensive theoretical and experimental research on the strength of isotropic materials, no single failure criterion has yet been found that applies to all isotropic materials under complex stress conditions.
[0005] Therefore, there is an urgent need to establish a failure criterion for isotropic materials (such as thermosetting, thermoplastic resins and metals) under complex stress states to meet engineering applications. Summary of the Invention
[0006] The purpose of this invention is to overcome the shortcomings of existing failure criteria for isotropic materials, such as low prediction accuracy, reliance on empirical parameters, and inconsistent expressions. This invention provides a failure prediction method applicable to isotropic materials. This method only requires two basic parameters, tensile strength and compressive strength, and does not require additional empirical parameters. It can accurately predict the failure envelope and fracture surface angle under complex stress states, and can also predict shear strength at the same time. It is applicable to brittle, semi-brittle, and ductile isotropic materials.
[0007] To achieve the above objectives, the present invention adopts the following technical solution:
[0008] A failure prediction method applicable to isotropic materials includes the following steps: To obtain the two fundamental strength values of isotropic materials: tensile strength and compressive strength ; Constructing the failure function The failure function is based on Mohr's theory, assuming that material failure is determined by stress components on its potential fracture surface, and that the potential fracture surface is parallel to the direction of the second principal stress; the expression for the failure function is:
[0009] in, The normal stress on the potential fracture surface, For the shear stress on the potential fracture surface, , , These are coefficients to be determined; The undetermined coefficients are determined using the two basic strength values, wherein: Using the hydrostatic loading assumption, which assumes that the material has a finite strength under hydrostatic tension and an infinite strength under hydrostatic compression, the following is derived: =0; The coefficients A and B are determined by uniaxial compressive loading and uniaxial tensile loading, and based on the ratio of compressive strength to tensile strength... Distinguishing between brittle and semi-brittle materials: When When the material is determined to be a semi-brittle material, The material was determined to be brittle. For a given stress state, at the potential fracture surface angle The range of values Internal calculation of the failure function The value of , and determine what makes Angle at maximum value The angle of the fracture surface is denoted as 1; if the maximum value is ≥1, the material is determined to have failed.
[0010] Furthermore, the stress components on the potential fracture surface , Calculate using the following formula:
[0011] in, The first principal stress, The third principal stress, The angle of the potential fracture surface.
[0012] Furthermore, the coefficient and Determine using the following formula:
[0013] in, For tensile strength, This refers to compressive strength.
[0014] Furthermore, the final expression of the failure function is: .
[0015] Furthermore, the fracture surface angle has analytical expressions under uniaxial tension and uniaxial compression, respectively: During uniaxial tension:
[0016] During uniaxial compression:
[0017] in, The fracture angle under uniaxial tension. This is the uniaxial compression fracture angle.
[0018] Furthermore, the method also includes predicting the shear strength of the material, which is determined according to the following formula:
[0019] Where S is the shear strength.
[0020] Furthermore, the method is applicable to thermosetting resins, thermoplastic resins, and metallic materials.
[0021] Furthermore, when predicting the failure envelope under complex stress states, the method obtains the failure boundary by calculating the maximum value of the failure function under different stress ratios.
[0022] Furthermore, the two fundamental strength values were determined through standard mechanical tests: tensile strength. The compressive strength was determined by uniaxial tensile testing. The test was conducted using a uniaxial compression test.
[0023] Furthermore, the method also includes: outputting prediction results, which include whether failure has occurred, the critical stress state at the time of failure, and the predicted fracture surface angle.
[0024] Compared with the prior art, the present invention has at least the following beneficial effects: 1. This invention requires only two basic parameters, tensile strength and compressive strength, and does not require shear strength or any empirical parameters. The parameter requirements are minimal, which greatly reduces the test cost and cycle.
[0025] 2. This invention employs a unified failure function expression. It does not distinguish between tensile and compressive failure modes, has a unified expression, and is easy to calculate.
[0026] 3. This invention is achieved through... The ratio automatically distinguishes between brittle and semi-brittle materials, and has wide applicability, covering a wide range of isotropic materials, including but not limited to thermosetting resins, thermoplastic resins, and metal materials.
[0027] 4. This invention can not only predict the failure envelope and fracture surface angle, but also analytically predict the shear strength. The prediction accuracy is significantly better than the classical Mohr-Coulomb criterion, and the prediction capability is strong.
[0028] 5. The present invention has concise analytical expressions for both the fracture surface angle and shear strength, which are highly analytical and convenient for engineering applications and numerical implementation. Attached Figure Description
[0029] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0030] Figure 1 This is a schematic diagram of stress components on the potential fracture surface of the material in an embodiment of the present invention; Figure 2 The failure prediction criteria and the Mohr-Coulomb criterion of this invention are applied to MY750 epoxy resin material ( =1.5) Comparison chart of predicted failure envelopes; Figure 3 The failure prediction criteria and the Mohr-Coulomb criterion of this invention are applied to metal materials such as copper and aluminum. ≈1.0) Prediction comparison chart of failure envelope. Detailed Implementation
[0031] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
[0032] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.
[0033] Example 1 This invention provides a failure prediction method applicable to isotropic materials, specifically including the following steps: Step 1: Obtain the basic strength parameters of the material This invention first obtains two fundamental strength values for isotropic materials: tensile strength. and compressive strength For example, these parameters are determined through standard mechanical tests: tensile strength The compressive strength was determined by uniaxial tensile testing. The test was conducted using a uniaxial compression test.
[0034] Step 2: Constructing a failure function based on Mohr's theory The embodiments of the present invention are based on Mohr's theory, which assumes that material failure is determined by the stress components on its potential fracture surface, and that the fracture surface is parallel to the direction of the second principal stress. The stress components on the fracture surface are completely determined by the first principal stress and the third principal stress. Figure 1 This diagram illustrates the stress components on the potential fracture surface of the material. Indicates the first principal stress. Indicates the third principal stress. Indicates the angle of the potential fracture surface.
[0035] like Figure 1 As shown, let the angle between the normal to the potential fracture surface and the direction of the first principal stress be . The stress components on the potential fracture surface include: normal stress. (Perpendicular to the fracture surface) and shear stress (Parallel to the fracture surface). The relationship between these stress components and the principal stresses is as follows: (1) In equation (1), The first principal stress, The third principal stress, Let be the angle of the potential fracture surface. This formula transforms the three-dimensional principal stress under any stress state into two independent stress components on the potential fracture surface, thereby simplifying the failure problem under complex stress states into a two-dimensional stress problem on the fracture surface.
[0036] This invention assumes that material failure is determined by stress components on its potential fracture surface, and thus constructs a failure function of the following form: (2) In equation (2) For failure function, This indicates that the material has failed.
[0037] The failure function is usually expanded into a power series of stress components and terminated at the second-order term. Since positive and negative shear have the same effect on failure, the first-order term of shear stress should be eliminated. At this time, the failure function expression is as follows: (3) in, The normal stress on the potential fracture surface, For the shear stress on the potential fracture surface, , , These are coefficients to be determined.
[0038] According to equations (1) and (3), the failure function is... It's about angles A periodic function with period . Therefore, it is only necessary to Find the failure function within the range The angle at which the maximum value is reached is the fracture surface angle. When the substrate fails, it is determined to be defective.
[0039] The failure function defined by equation (3) is sufficiently smooth. Within one cycle, the maximum value is the maximum value. Therefore, when fracture occurs under a certain stress state, the following condition is satisfied: (4) In equation (4), The angle of the fracture surface.
[0040] Step 3: Determine the undetermined coefficients The embodiments of the present invention use two basic strength values: tensile strength. and compressive strength The undetermined coefficients in equation (3) are uniquely determined without requiring any empirical parameters. The process for determining the undetermined coefficients is as follows: Static water loading assumption: This invention makes the following assumptions regarding hydrostatic loading: Under hydrostatic tensile stress, the material strength is finite; while under hydrostatic compression, the strength is infinite. (The last sentence appears to be incomplete and possibly refers to a different concept.) ( (representing the second principal stress), according to equation (1), the stress components on the potential fracture surface are: (5) Substituting equation (5) into equation (3), we get: (6) when hour, This shows that the material strength is infinitely large under hydrostatic tension, which is clearly unreasonable. When When, equation (6) must have two real roots. and : (7) This indicates that the hydrostatic tensile strength is The hydrostatic compressibility is This contradicts the assumption. Therefore, we can deduce that: (8) As can be seen from equation (8), the physical meaning of this assumption is that isotropic materials usually do not break under hydrostatic compression (triaxial isobaric) but have limited breaking strength under hydrostatic tension.
[0041] Single-axis compression loading: This invention's embodiments consider compressive loading leading to material failure. According to equation (1), the stress components on the potential fracture surface are: (9) Let the failure function be defined. F exist hour( (For uniaxial compression fracture angle), reaching a maximum value of 1. Substituting equation (9) into equation (3), and using the conditions of equation (4), we can obtain: (10) (11) (12) When a material fractures under compression, the angle between the fracture surface and the loading direction is generally not equal to 0° or 90°. Therefore, equation (11) can be simplified to: (13) Substituting equation (13) into equations (10) and (12), we get: (14) (15) This leads to the relationship between coefficients A and B.
[0042] Uniaxial tensile loading: This invention considers uniaxial tensile loading to material failure. According to equation (1), the stress components on the potential fracture surface are: (16) Let the failure function be defined. exist hour( (For uniaxial tensile fracture angle), reaching a maximum value of 1. Substituting equation (16) into equation (3), we can obtain the following from the condition in equation (4): (17) (18) (19) From equation (18), we can obtain: (20) or: (twenty one) when Then, equation (17) can be simplified to: (twenty two) Substituting equation (22) into equation (14), we get: (twenty three) Substituting equations (22) and (23) into equation (19), we get: (twenty four) Therefore, we can conclude that: (25) when At that time, that is: (26) At this point, equation (17) can be simplified to: (27) Solving equations (14) and (27) simultaneously yields: (28) Substituting equation (28) into equation (19), we get: (29) In particular, When equations (20) and (21) are satisfied simultaneously, the undetermined coefficients are... , Since they have the same value, they can be used to distinguish between semi-brittle and brittle materials. Therefore, according to The ratio of the materials is used to classify materials into two categories in this embodiment of the invention: when At that time, the material is considered a semi-brittle material. In this case, the material is considered brittle. This differentiation mechanism allows the invention to be adaptively applied to different categories of materials without requiring the user to pre-specify the material type.
[0043] Based on the above derivation, Substituting these values, we obtain the final expression for the failure function, thus determining the failure prediction criterion of the method described in this embodiment of the invention: (30) This failure function It contains only the first term of normal stress and the second term of shear stress, making it concise in form. It also uses a unified expression for tensile and compressive stresses, overcoming the shortcomings of existing criteria that require distinguishing between tensile and compressive failures.
[0044] Among them, coefficient and The final expression is: (31) The derivation of this formula ensures the theoretical rigor of the criterion, while also allowing the coefficients to be determined analytically entirely from the basic strength values, without the need for any experimental fitting.
[0045] Step 4: Failure Prediction For a given stress state, first calculate the principal stresses. , , And determine its direction; the angle range between the inclined surface and the direction of the first principal stress is as follows: Calculate the included angles according to formula (1) Stress components on the inclined surface Substitute into the failure function (30) to find the cause. Angle that achieves the maximum value If the maximum value is ≥1, then the material is considered to have failed. This is the predicted fracture surface angle.
[0046] The embodiments of the present invention also provide analytical expressions for the fracture surface angles under uniaxial tension and uniaxial compression: During uniaxial tension: (32) During uniaxial compression: (33) in, This is the fracture angle under uniaxial tension, and the corresponding expression is given for uniaxial tension. For uniaxial compression fracture angle, the corresponding expression is given for uniaxial compression; in particular, when hour, This analytical expression allows for the direct acquisition of fracture surface angles under uniaxial loading without numerical searching, greatly facilitating engineering applications.
[0047] Step 5: Shear Strength Prediction The method described in this embodiment of the invention can also predict the shear strength of materials. Considering pure shear loading to failure (… At this point, the principal stresses are: (34) in, Let be the shear strength. According to equation (1), the stress components on the potential fracture surface are as follows: (35) Let the failure function be defined. exist hour( (where the shear fracture angle is 1), reaching its maximum value. Substituting equation (35) into equation (3), we can obtain the following from the condition in equation (4): (36)() (37) (38) Solving equation (37) yields: (39) or: (40) when Then, equation (36) simplifies to: (41) thereby: (42) From equation (38), we can obtain: (43) when Substituting equation (31) into equation (43) yields: (44) Therefore, this situation does not exist.
[0048] when Substituting equation (31) into equation (43) yields: (45) Therefore, we can solve for: (46) when hour: (47) Substituting equation (47) into equation (36) and solving, we get: (48) Substituting equations (47) and (48) into equation (38) yields: (49) when Substituting equation (31) into equation (49), we get: (50)() when Substituting equation (31) into equation (49), we get: (51) Based on the above criteria according to embodiments of the present invention, the shear strength can be derived. and shear fracture angle The expression is: (52) in and It is determined by equation (31). This feature enables the embodiments of the present invention to analytically predict shear strength when only the tensile and compressive strengths are known, which is a function not available in the classical Mohr-Coulomb criterion and has important engineering practical value.
[0049] The final prediction result output of the method described in this embodiment of the invention includes whether material failure has occurred, the critical stress state at the time of failure, and the predicted fracture surface angle.
[0050] The following examples of different isotropic materials illustrate the effectiveness of the failure prediction method established in this invention for predicting the failure of isotropic materials.
[0051] Example 2 This embodiment uses the MY750 epoxy resin material disclosed in the literature as an example to illustrate the effectiveness of the failure prediction method established in this embodiment for semi-brittle thermosetting resins. The method described in this invention is applicable to various isotropic materials, including but not limited to thermosetting resins, thermoplastic resins, and metallic materials. This embodiment and subsequent embodiments respectively demonstrate typical types among them.
[0052] Material parameters: Tensile strength of MY750 epoxy resin =80MPa, compressive strength =120MPa, shear strength =54MPa (for comparative verification).
[0053] Material type determination: Calculation =120 / 80=1.5, which belongs to The range is such that the material belongs to the semi-brittle material category, and the formula (31) is used. The formula is used to calculate the coefficients.
[0054] Calculation of undetermined coefficients: =8( - ) / ( + )²=8×40 / (200)²=320 / 40000=0.008 MPa - ¹ =16 / ( + )²=16 / 40000=0.0004 MPa - ² Failure envelope prediction: For a series of different stress states (such as different ratios of normal stress and shear stress), embodiments of the present invention calculate the failure function under different stress ratios. The maximum value is used to obtain the failure boundary.
[0055] like Figure 2 As shown in the figure, the horizontal axis represents the material's properties at... The ratio of axial stress to tensile strength (where, Axial stress = (axial stress), ordinate represents The ratio of axial stress to tensile strength. As can be seen from the figure, the failure envelope of the MY750 material predicted by the failure prediction method described in this embodiment of the invention agrees well with the experimental data reported in the literature. The classic Mohr-Coulomb criterion has a large deviation in its predictions for this type of semi-brittle material, especially in the tensile-dominant and compressive-dominant regions. The criterion in this embodiment of the invention uses a quadratic failure function based on fracture surface stress analysis, adaptively adjusting the coefficient calculation formula, and utilizing... The ratio automatically distinguishes material types, thus more accurately describing the actual failure mechanism of materials and successfully achieving high-precision prediction of semi-brittle materials.
[0056] Example 3 This embodiment uses copper, aluminum, and other near-perfectly ductile metals as examples to illustrate the application of this invention. ≈1.0 Material suitability.
[0057] Material parameters: For metallic materials such as copper and aluminum, their tensile strength and compressive strength are approximately equal, i.e. ≈1.0.
[0058] Material type determination: due to ≈1.0, belongs to The range is such that the coefficients are calculated using the same formula for the semi-brittle material branch. When When = 1, =8(1-1) / (1+1)² = 0, =16 / (1+1)²=4. At this point, the failure function simplifies to... ,Right now =0.5.
[0059] Failure envelope prediction: such as Figure 3 As shown in the figure, the horizontal axis represents the ratio of normal stress to tensile strength, and the vertical axis represents the ratio of shear stress to tensile strength. It can be seen from the figure that the failure prediction method described in this embodiment of the invention predicts the failure envelope of metallic materials in good agreement with experimental data. The classic Mohr-Coulomb criterion... The predicted material value of ≈1.0 deviates somewhat from the experimental data. The prediction accuracy is significantly improved in the embodiments of this invention due to the use of a more accurate quadratic function form.
[0060] In summary, the failure prediction method provided by the embodiments of the present invention can be applied to the structural strength assessment of resin matrices (thermosetting / thermoplastic) and metallic materials, and can also be embedded in the user material subroutine of finite element software to realize progressive damage analysis of isotropic materials under complex loads.
[0061] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, various modifications and variations can be made to the embodiments of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A failure prediction method applicable to isotropic materials, characterized in that, Includes the following steps: To obtain the two fundamental strength values of isotropic materials: tensile strength and compressive strength ; Constructing the failure function The failure function is based on Mohr's theory, assuming that material failure is determined by stress components on its potential fracture surface, and that the potential fracture surface is parallel to the direction of the second principal stress; the expression for the failure function is: in, The normal stress on the potential fracture surface, For the shear stress on the potential fracture surface, , , These are coefficients to be determined; The undetermined coefficients are determined using the two basic strength values, wherein: Using the hydrostatic loading assumption, which assumes that the material has a finite strength under hydrostatic tension and an infinite strength under hydrostatic compression, the following is derived: =0; The coefficients were determined by uniaxial compressive and tensile loading. and And based on the ratio of compressive strength to tensile strength Distinguishing between brittle and semi-brittle materials: When When the material is determined to be a semi-brittle material, The material was determined to be brittle. For a given stress state, at the potential fracture surface angle The range of values Internal calculation of the failure function The value of , and determine what makes Angle at maximum value The angle of the fracture surface is denoted as 1; if the maximum value is ≥1, the material is determined to have failed.
2. The method according to claim 1, characterized in that, Stress components on the potential fracture surface , Calculate using the following formula: in, The first principal stress, The third principal stress, The angle of the potential fracture surface.
3. The method according to claim 1, characterized in that, coefficient and Determine using the following formula: in, For tensile strength, This refers to compressive strength.
4. The method according to claim 3, characterized in that, The final expression of the failure function is: .
5. The method according to claim 1, characterized in that, The fracture surface angle has analytical expressions under uniaxial tension and uniaxial compression, respectively: During uniaxial tension: During uniaxial compression: in, The fracture angle under uniaxial tension. This is the uniaxial compression fracture angle.
6. The method according to claim 1, characterized in that, The method further includes predicting the shear strength of the material, which is determined according to the following formula: Where S is the shear strength.
7. The method according to claim 1, characterized in that, The method is applicable to thermosetting resins, thermoplastic resins, and metallic materials.
8. The method according to claim 1, characterized in that, When predicting the failure envelope under complex stress states, the method obtains the failure boundary by calculating the maximum value of the failure function under different stress ratios.
9. The method according to claim 1, characterized in that, The two basic strength values were determined through standard mechanical tests: tensile strength. The compressive strength was determined by uniaxial tensile testing. The test was conducted using a uniaxial compression test.
10. The method according to claim 1, characterized in that, The method further includes: outputting prediction results, which include whether material failure has occurred, the critical stress state at the time of failure, and the predicted fracture surface angle.