CN113514351B - Fatigue crack propagation behavior prediction method considering prestress redistribution - Google Patents
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Abstract
The invention discloses a fatigue crack propagation behavior prediction method considering prestress redistribution, belonging to the technical field of material science and engineering application. According to the method, state values such as initial prestress, plastic strain and back stress are introduced into a finite element model containing initial cracks, and then the maximum stress intensity factor at the crack tip in one loading period is determined, so that a crack expansion angle theta and a loading period N under a preset crack expansion increment are obtained. Loading the current model for N times, extracting a state value at an integration point after stress redistribution, updating a grid model after the dl length of crack expansion, mapping the extracted state value into a new grid model, repeating the steps to finish fatigue crack expansion behavior prediction, and solving the actual engineering problem in the field of fatigue crack expansion of the parts after surface treatment according to the obtained prediction result. The method can realize fatigue crack propagation behavior prediction under the influence of the prestress redistribution rule, and has the advantage of high precision.
Description
Technical Field
The invention relates to a fatigue crack growth behavior prediction method considering prestress redistribution, in particular to a fatigue crack growth behavior prediction method of an experimental component which is treated by a surface strengthening technology and then introduces prestress, belonging to the technical fields of material science and engineering application.
Background
At present, the means for improving the fatigue crack growth life of parts in engineering mainly utilizes surface engineering technology to improve the surface material performance, such as cold spraying treatment, shot peening, carburizing treatment and the like. Many parts in the engineering are subjected to surface engineering treatment in order to improve fatigue strength. Such as blades in aeroengines, barrels, connecting bolts, gears, connecting rods in diesel engines, crankshafts, etc. These surface treatments all introduce a pre-stress in the surface layer of the material for counteracting the fatigue tensile stress, so that the fatigue life of the component is greatly improved. The induced prestressing is generally regarded as an additional safety factor in engineering, and the life improvement caused by residual stress is not considered when the fatigue life is carried out. Therefore, the fatigue crack growth behavior prediction method under the influence of the prestress redistribution rule is considered, so that the fatigue life improvement degree under the influence of the prestress can be quantized, and the guiding significance is further generated for the fatigue life design.
The problem of predicting fatigue crack growth behavior of parts subjected to surface engineering treatment and then subjected to prestress introduction is solved, and prestress redistribution in the crack growth process is generally ignored. The parts are subjected to plastic deformation under the action of fatigue load, and the plastic deformation is a major factor of the redistribution phenomenon of the prestress. When the crack is generated and continuously propagates, a new free surface is generated in the part, and the new free surface also releases part of residual prestress so as to cause prestress redistribution.
Disclosure of Invention
The invention aims to provide a fatigue crack growth behavior prediction method considering prestress redistribution, which considers the fatigue crack growth life prediction under the prestress redistribution caused by two factors of plastic deformation and free surface formation in the whole life cycle of a part from plastic deformation to crack growth when predicting the prestress-containing fatigue crack growth behavior, and improves the prediction precision of the crack growth life.
The invention aims at realizing the following technical scheme:
the invention discloses a fatigue crack growth behavior prediction method considering prestress redistribution, which comprises the following steps:
Step 1, building a member finite element model containing initial cracks, and setting load conditions, boundary conditions and material parameters;
Further, the initial crack length is far smaller than the thickness of the pre-stress layer introduced by the surface strengthening treatment, and the initial crack length l 0 and the initial angle theta 0 are determined according to practical conditions;
step 2, introducing initial prestress, initial plastic strain and initial back stress into a finite element model of the component containing the initial crack;
step 3, determining a maximum stress intensity factor K of a crack tip in a loading period, and determining a crack expansion angle theta and a loading period dN required under a preset crack expansion increment;
step 3.1, applying a far-end fatigue load sigma B to the finite element model, and determining a maximum stress intensity factor K value of a crack tip by a girth integration method when the load amplitude reaches the maximum;
Step 3.2, determining a crack expansion angle theta and a loading period dN required under a preset crack expansion increment dl according to actual conditions;
the crack propagation angle θ is given by formula (1):
Wherein, theta i is the angle of the crack at the ith turning point, theta i-1 is the angle of the crack at the ith-1 th turning point, and K Imaxi and K IImaxi are the maximum stress intensity factors of the type I and type II cracks at the ith turning point respectively;
the required loading period dN at the preset crack growth increment dl is derived by equation (2):
dl/dN＝A(ΔK)n (2)
wherein a and n are material dependent coefficients;
Step 4, carrying out dN times of fatigue load loading and unloading processes on the current model, and extracting residual stress values, residual plastic strain, back stress values and integral point coordinates at integral points of the finite element model after the residual stress redistribution phenomenon occurs after the fatigue load loading and unloading processes are finished;
step 5, updating the grid model with the crack occurrence expansion length of dl;
step 5.1, extracting a finite element grid model after the occurrence of the prestress redistribution phenomenon through the residual stress value, the residual plastic strain, the back stress value and the integral point coordinates at the integral points of the finite element model after the occurrence of the residual stress redistribution phenomenon determined in the step 4;
step 5.2, updating the crack tip position and the crack path in the finite element grid model after the residual stress redistribution phenomenon occurs through the crack expansion angle theta and the preset crack expansion increment dl determined in the step3, and re-dividing the grid;
step 5.3, extracting the position of the crack tip and the coordinate value of the integral point of the finite element model after updating the crack path;
Step 6, optimizing a grid interpolation method, and mapping the residual prestress value, the residual plastic strain and the back stress value extracted in the step 4 into a new grid model by combining the coordinate position of the integral point of the finite element grid model after the residual stress redistribution phenomenon in the step 4 and the coordinate value of the integral point of the finite element model after the crack tip position and the crack path update in the step 5.3;
And 7, repeating the iterative process of the steps 3-6 until the crack length l reaches a preset critical value, and completing fatigue crack growth behavior prediction under the influence of a prestress redistribution rule.
And step 8, according to the fatigue crack growth behavior prediction result under the influence of the prestress redistribution rule, which is obtained in the step 7, the actual engineering problem in the field of fatigue crack growth of the parts which are subjected to surface engineering technology treatment and introduced with prestress is solved.
Further, the solving the actual engineering problem in the field of fatigue crack growth of the parts comprises: and the material damage tolerance design, the structural safety evaluation and the structural residual life prediction are realized by solving the engineering problems, so that the service life of the material is fully exerted.
The beneficial effects are that:
1. The invention discloses a fatigue crack growth behavior prediction method considering prestress redistribution, which considers the prestress redistribution caused by plastic deformation in the loading process and the prestress redistribution phenomenon caused by the generation of a new crack surface into each fatigue crack growth increment extraction. Under the condition that the fatigue load amplitude is unchanged, the change of the prestress distribution condition can influence the stress state of the crack tip, the stress intensity factor K of the crack tip is obtained based on the prestress distribution condition after the redistribution phenomenon occurs under the current loading cycle number, further, the crack expansion angle and the fatigue life time required by each crack expansion increment are obtained, and the prediction precision is improved.
2. According to the fatigue crack growth behavior prediction method considering the prestress redistribution, according to the obtained fatigue crack growth behavior prediction result considering the influence of the prestress redistribution, the influence degree of the prestress on the fatigue crack growth rule under the action of different load amplitude values can be further obtained, and the actual engineering problem in the field of fatigue crack growth of parts containing the prestress is solved.
Drawings
FIG. 1 is a flow chart of a fatigue crack growth behavior prediction method taking into account prestress redistribution according to the present invention;
FIG. 2 is a finite element model diagram of a component containing an initial crack;
FIG. 3 is a finite element model diagram of a detail of a crack site including an initial crack member;
FIG. 4 is a graph of initial prestress values for a component containing initial cracks;
FIG. 5 is a graph of initial back stress values along the depth direction for an initial crack-containing member;
FIG. 6 is a graph showing the distribution of prestress values in the vicinity of a crack in the depth direction when the crack length l of a member containing an initial crack reaches a preset critical value;
FIG. 7 is a graph comparing crack growth life predictions for a method of the present invention and without consideration of stress redistribution.
Detailed Description
For a better description of the objects and advantages of the present invention, the following description of the invention refers to the accompanying drawings and examples.
Example 1:
as shown in fig. 1, the fatigue crack growth behavior prediction method considering prestress redistribution disclosed in this embodiment includes the following steps:
step 1, establishing a finite element model containing an initial crack component:
As shown in FIG. 2, the finite element model of the member containing initial cracks of the embodiment is a rectangular finite element model with the thickness of 4mm multiplied by 40mm, the elastic modulus of the structure is 210000MPa, and the initial yield strength is 450MPa;
as shown in fig. 3, an initial crack is provided at a central position of the surface of the member, the initial crack length is 10 μm, and the crack initiation angle is set to be perpendicular to the surface of the member;
step 2, introducing initial prestress, initial plastic strain and initial back stress into the finite element model:
wherein the initial pre-stress is introduced into the model by the user subroutine SIGINI of the ABAQUS software and the initial residual plastic strain and initial back stress are introduced into the model by the user subroutine HARDINI of the ABAQUS software;
In this embodiment, the material constitutive model adopts a follow-up hardening model, so that initial plastic strain is not required to be introduced, an initial prestress value is shown in fig. 4, and an initial back stress value is distributed along the depth direction as shown in fig. 5;
Step 3, determining a maximum stress intensity factor K of the crack tip in one loading period, and determining a crack expansion angle theta and a loading period dN required under a preset crack expansion increment dl:
Step 3.1, applying a far-end fatigue load sigma B =500 MPa to the finite element model, and when the load amplitude reaches the maximum, determining a crack tip stress intensity factor K value by using a girth integration method, and outputting the crack tip maximum stress intensity factor K value by using ABAQUS software;
step 3.2, crack growth angle θ and loading period dN required at preset crack growth increment dl:
the crack propagation angle θ is given by formula (1):
Wherein, theta i is the angle of the crack at the ith turning point, theta i-1 is the angle of the crack at the ith-1 th turning point, and K Imaxi and K IImaxi are the maximum stress intensity factors of the type I and type II cracks at the ith turning point respectively;
the required loading period dN at the preset crack growth increment dl is derived by equation (2):
dl/dN＝A(ΔK)n (2)
wherein a and n are material dependent coefficients;
Step 4, carrying out a fatigue load loading and unloading process on the current finite element model for 100 times, and extracting a residual stress value, a residual plastic strain, a back stress value and an integral point coordinate at an integral point of the finite element model after the residual stress redistribution phenomenon occurs by using a user subroutine UMAT of ABAQUS software after the completion of the fatigue load loading and unloading process;
step 5, updating the grid model after the crack occurrence dl=5μm expansion length:
Step 5.1, extracting a finite element grid model after the prestress redistribution phenomenon occurs through the ABAQUS result file completed in the step 4;
Step 5.2, updating crack tip positions and crack paths in the finite element grid model after the residual stress redistribution phenomenon occurs by combining the crack expansion angle theta and the preset crack expansion increment dl determined in the step 3 with a PYTHON script, and re-dividing the grid;
step 5.3, extracting the position of the crack tip and the coordinate value of the integral point of the finite element model after updating the crack path by using a user subroutine UMAT of ABAQUS software;
step 6, mapping the residual prestress value, residual plastic strain and back stress value extracted in the step 4 into a new grid model by utilizing a grid interpolation method and combining the coordinate position of the integral point of the finite element grid model after the stress redistribution phenomenon in the step 4 and the coordinate value of the integral point of the finite element model after the crack tip position and the crack path update in the step 5.3;
And 7, repeating the iterative processes of the steps 3 to 6 until the crack length l=40 mu m reaches a preset critical value, so as to complete fatigue crack growth behavior prediction under the influence of a prestress redistribution rule, and when the crack length l reaches the preset critical value, the distribution rule of the prestress values near the crack along the depth direction is shown in fig. 6.
As shown in fig. 7, crack propagation life prediction comparison with consideration of prestress redistribution, without consideration of prestress redistribution, and without consideration of prestress at all: when the prestress is not considered at all, the inhibition effect of the prestress on the fatigue crack expansion is ignored, and the predicted life value is minimum; when the prestress is considered but the prestress redistribution is not considered, the prestress counteracts partial fatigue tensile stress to cause insufficient fatigue load to enable crack to develop, and the predicted service life is infinite; when the prestress redistribution is considered, the counteracting effect of residual prestress on fatigue load is weakened, crack is expanded, and the predicted life value is larger than the predicted value which does not consider prestress at all. For comprehensive analysis, the prestress redistribution is considered to be more in line with the actual situation, so that the use potential of the structure can be further excavated.
While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.
Claims (2)
1. A fatigue crack growth behavior prediction method considering prestress redistribution is characterized in that: the method comprises the following steps:
Step 1, building a member finite element model containing initial cracks, and setting load conditions, boundary conditions and material parameters;
The initial crack length is far smaller than the thickness of the pre-stress layer introduced by the surface strengthening treatment, and the initial crack length l 0 and the initial angle theta 0 are determined according to actual conditions;
Step 2, introducing initial prestress, initial plastic strain and initial back stress into the finite element model;
step 3, determining a maximum stress intensity factor K of a crack tip in a loading period, and determining a crack expansion angle theta and a loading period N required under a preset crack expansion increment;
step 3.1, applying a far-end fatigue load sigma B to the finite element model, and determining a maximum stress intensity factor K value of a crack tip when the load amplitude reaches the maximum;
Step 3.2, determining a crack expansion angle theta and a loading period dN required under a preset crack expansion increment dl according to actual conditions;
the crack propagation angle θ is given by formula (1):
Wherein, theta i is the angle of the crack at the ith turning point, theta i-1 is the angle of the crack at the ith-1 th turning point, and K Imaxi and K IImaxi are the maximum stress intensity factors of the type I and type II cracks at the ith turning point respectively;
the required loading period dN at the preset crack growth increment dl is derived by equation (2):
dl/dN＝A(ΔK)n (2)
wherein a and n are material dependent coefficients;
Step 4, carrying out dN times of fatigue load loading and unloading processes on the current model, and extracting residual stress values, residual plastic strain, back stress values and integral point coordinates at integral points of the finite element model after the residual stress redistribution phenomenon occurs after the fatigue load loading and unloading processes are finished;
step 5, updating the grid model with the crack occurrence expansion length of dl;
step 5.1, extracting a finite element grid model after the occurrence of the prestress redistribution phenomenon through the residual stress value, the residual plastic strain, the back stress value and the integral point coordinates at the integral points of the finite element model after the occurrence of the residual stress redistribution phenomenon determined in the step 4;
step 5.2, updating the crack tip position and the crack path in the finite element grid model after the residual stress redistribution phenomenon occurs through the crack expansion angle theta and the preset crack expansion increment dl determined in the step3, and re-dividing the grid;
step 5.3, extracting the position of the crack tip and the coordinate value of the integral point of the finite element model after updating the crack path;
Step 6, mapping the residual prestress value, the residual plastic strain and the back stress value extracted in the step 4 into a new grid model by combining the integral point coordinate position of the finite element grid model after the residual stress redistribution phenomenon in the step 4 and the integral point coordinate value of the finite element model after the crack tip position and the crack path updating in the step 5.3;
Step 7, repeating the iterative process of the step 3-step 6 until the crack length l reaches a preset critical value, and completing fatigue crack growth behavior prediction under the influence of a prestress redistribution rule;
the method also comprises a step 8 of solving the actual engineering problem in the field of fatigue crack growth of the parts which are subjected to surface engineering treatment and introduced with the prestress according to the fatigue crack growth behavior prediction result under the influence of the prestress redistribution rule;
The actual engineering problems in the field of fatigue crack propagation of the parts, which are treated by the surface engineering technology and are induced with prestress, comprise structural damage tolerance analysis and structural residual life prediction, and the service life of the structure is fully exerted by solving the engineering problems.
2. A fatigue crack growth behavior prediction method considering prestress redistribution as claimed in claim 1, wherein: in the step 4, the workload of simulating each loading and unloading process is large, and the residual prestress value in the model tends to be stable after loading for a plurality of cycles, and only fewer loading and unloading processes are required to be simulated.
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