CN104951633A - Method for predicting work-hardening and dynamic recovery behaviors of nickel-based alloy - Google Patents

Abstract

The invention discloses a method for predicting work-hardening and dynamic recovery behaviors of nickel-based alloy. The method comprises the following steps: (1), obtaining true stress-true strain data of the nickel-based alloy through a high-temperature compression test; (2), establishing a mathematical model for predicting the work-hardening and dynamic recovery behaviors of the nickel-based alloy; (3), determining a relationship among the yield stress, deformation temperature, strain rate and initial grain size of the nickel-based alloy according to deformation conditions of the high-temperature compression test and the true stress-true strain data of the nickel-based alloy and determining a relationship between stress caused by dislocation density and dislocation density in the nickel-based alloy; (4), predicting the work-hardening and dynamic recovery behaviors of the nickel-based alloy under any deformation condition by using a numerical difference principle, an iteration accumulation method and the like. By adopting the method, the work-hardening and dynamic recovery behaviors of the nickel-based alloy can be rapidly and accurately predicted, and important technical guidance significance on reasonably making a nickel-based alloy processing technology is realized.

Description

A kind of method predicting nickel-base alloy work hardening and dynamic recovery behavior

Technical field:

The invention belongs to nickel-base alloy processing engineering technology field, relate to a kind of method predicting nickel-base alloy work hardening and dynamic recovery behavior.

Background technology:

In nickel-base alloy hot procedure, the thermal deformation process of nickel-base alloy can be divided into elastic deformation and two stages of plastic yield usually.The elastic deformation stage of nickel-base alloy can pass through Hooke's law accurate description usually.When plus load has exceeded the yield stress of nickel-base alloy, the plastic yield showing as nickel-base alloy on a macroscopic scale starts to occur, and shows as the dislocation motion process of nickel-base alloy inside on a microscopic scale.Due to the work hardening behavior that generation and the propagation of dislocation cause, further promote the increase of nickel-base alloy trus stress; Along with the increase of deformation extent, room is progressively spread, and the dynamic recovery process of the dislocation annihilation that slip of dislocation and climbing causes and dislocation rearrangement starts to occur.Research show the work hardening of nickel-base alloy and dynamic recovery behavior very complicated, be significantly subject to deformation temperature, the combined influence of the Deformation Parameters such as strain rate and strain.Work hardening and dynamic recovery are as kind of the typical mechanism of two in nickel-base alloy thermal deformation process, and numerous scholar has carried out great many of experiments and theoretical research work, have invented the method for the work hardening of multiple prediction nickel-base alloy and dynamic recovery behavior.Wherein, Arrhenius model, Cingara model and relevant correction model can nickel-base alloy work hardening under the desirable heat deformable state such as accurate description constant temperature constant strain rate and dynamic recovery behaviors, but are difficult to promote the use of the actual hot procedure of industry becoming deformation behaviour when having.Article " Analysis of the work-hardening behavior of C-Mn steels deformed under hot-working conditions " (author: E.S.Puchi-Cabrera, M.H.Staia, J.D.Gu é rin, 2013 (51) " International Journal of Plasticity ") in, become the mathematical model of the C-Mn steel work hardening behavior deformation condition when author proposes a kind of prediction from the angle of macroscopical Deformation Parameters.But there is no both at home and abroad and saw based on nickel-base alloy thermal deformation Physical Mechanism, propose to predict the method for nickel-base alloy work hardening and dynamic recovery behavior under random variation condition.

Therefore, the present invention is from nickel-base alloy thermal deformation Physical Mechanism, invent a kind of method can predicting nickel-base alloy work hardening and dynamic recovery behavior under random variation condition, to solve existing Forecasting Methodology range of application narrow, be difficult to the drawback realizing engineer applied.The invention of the method and apply and have important technological guidance's meaning to rational nickel-base alloy heat processing technique.

Summary of the invention:

The object of the present invention is to provide a kind of method predicting nickel-base alloy work hardening and dynamic recovery behavior, solve existing Forecasting Methodology range of application narrow, be difficult to the drawback that engineering is promoted, have important technological guidance's meaning to rational nickel-base alloy heat processing technique.

For achieving the above object, the technical solution used in the present invention is: a kind of method predicting nickel-base alloy work hardening and dynamic recovery behavior.The concrete steps of the method are:

Step 1: be 900 DEG C ~ 1100 DEG C and strain rate in deformation temperature be 0.0005s ^-1~ 10s ^-1thermal deformation conditions under, high temperature compressed experiment is carried out to the nickel-base alloy that Initial Grain Size is 20 μm ~ 90 μm, obtains the true stress-true strain data of nickel-base alloy;

Step 2: the mathematical model setting up prediction nickel-base alloy work hardening and dynamic recovery behavior:

$\left\{\begin{array}{c}\mathrm{\σ}={\mathrm{\σ}}_y+{\mathrm{\σ}}_i\\ {\mathrm{\σ}}_y=A_y{d}_0^{m_y}{\left(\stackrel{\·}{\mathrm{\ϵ}}\exp (Q_y/\mathrm{RT})\right)}^{n_y}\\ {\mathrm{\σ}}_i=\mathrm{M\α\μb}\sqrt{{\mathrm{\ρ}}_i}\\ {\stackrel{\·}{\mathrm{\ρ}}}_i=M(\sqrt{{\mathrm{\ρ}}_i}/k_w+1/d_0)\stackrel{\·}{\mathrm{\ϵ}}/b-f_v{\mathrm{\ρ}}_i\stackrel{\·}{\mathrm{\ϵ}}\\ k_w=A_w{d}_0^{m_w}{\left(\stackrel{\·}{\mathrm{\ϵ}}\exp (Q_w/\mathrm{RT})\right)}^{n_w}\\ f_v=A_v{d}_0^{m_v}{\left(\stackrel{\·}{\mathrm{\ϵ}}\exp (Q_v/\mathrm{RT})\right)}^{n_v}\end{array}\right.$

Wherein σ _yfor yield stress, σ _ifor the stress that dislocation desity causes, M is Taylor coefficients, and α is dislocation interactions constant, and μ is material modulus of shearing, and b is Bai Shi vector, and R is unified gas law constant, ρ _ifor dislocation desity, for dislocation desity develops speed, k _wand f _vbe respectively strain hardening coefficient and dynamic recovery coefficient; A _y, A _w, A _v, m _y, m _w, m _v, n _y, n _w, n _v, Q _y, Q _wand Q _vbe material parameter;

Step 3: according to the deformation condition of high temperature compressed experiment and the true stress-true strain data of nickel-base alloy, set up the yield stress σ of nickel-base alloy _ywith alternating temperature temperature T, strain rate initial Grain Size d ₀between relation, namely ln σ _y-1/T and ln σ _y-lnd ₀graph of a relation, and the method determination material parameter A passing through linear fit _y, m _y, n _yand Q _yconcrete numerical value;

Utilize diff principle, by the dislocation desity increment Delta ρ caused with arbitrarily small strain increment Δ ε _tbe expressed as with stress increment Δ σ with Δ σ=(α M μ b ρ _i ^-1/2) Δ ρ _i/ 2, write iteration accumulation algorithm program, embed numerical simulation software, in conjunction with the true stress-true strain data of nickel-base alloy, be optimized and solve, determine the material parameter A predicted in the mathematical model of nickel-base alloy work hardening and dynamic recovery behavior _w, A _v, m _w, m _v, n _w, n _v, Q _wand Q _vconcrete numerical value;

Step 4: the prediction nickel-base alloy work hardening that the material parameter substitution step 2 that step 3 is determined is set up and the mathematical model of dynamic recovery behavior, utilize diff principle, write iteration accumulation algorithm program, embed numerical simulation software, realize the renewal of material parameter at any iteration step of Deformation Parameters and temperature distortion parameter influence, and then the work hardening of nickel-base alloy and dynamic recovery behavior under prediction random variation condition, wherein Deformation Parameters comprises deformation temperature and strain rate, and the material parameter of temperature distortion parameter influence comprises yield stress σ _y, strain hardening coefficient k _wwith dynamic recovery coefficient f _v.

The present invention is by the high temperature compressed experiment of nickel-base alloy, on dislocation desity theoretical model basis, establish the mathematical model of a kind of nickel-base alloy work hardening of prediction and dynamic recovery behavior, take into full account the impact of real-time deformation condition on nickel-base alloy hot deformation behavior, when to achieve pair, become the quick and precisely prediction of nickel-base alloy work hardening and dynamic recovery behavior under deformation condition.

Beneficial effect of the present invention is: the present invention has taken into full account the impact of real-time deformation condition on nickel-base alloy hot deformation behavior, the quick and precisely prediction of nickel-base alloy work hardening and dynamic recovery behavior under deformation condition is become when to achieve pair, can apply in the actual hot procedure of industry of then distortion, solve existing Forecasting Methodology range of application narrow, be difficult to the drawback realizing engineer applied.The invention of the method and apply rational nickel-base alloy heat processing technique significant.

Accompanying drawing illustrates:

Fig. 1 ln σ _ywith graph of a relation

Fig. 2 ln σ _ywith 1/T graph of a relation

Fig. 3 ln σ _ywith lnd ₀graph of a relation

Under Fig. 4 constant temperature constant strain rate condition, the work hardening of GH4169 alloy and dynamic recovery behavior predicts the outcome

Predicting the outcome of the work hardening of GH4169 alloy and dynamic recovery behavior under deformation condition is become during Fig. 5

Embodiment:

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

The present invention is a kind of method predicting nickel-base alloy work hardening and dynamic recovery behavior, example is predicted as below with the work hardening of GH4169 alloy (typical nickel-base alloy) and dynamic recovery behavior, the concrete implementation detail of the Forecasting Methodology that detailed introduction the present invention relates to, its method comprises:

Step 1: carry out high temperature compressed experiment to GH4169 alloy, Initial Grain Size is respectively 75 μm, 48 μm and 33 μm, and deformation temperature is respectively 920 DEG C, 950 DEG C, 980 DEG C, 1010 DEG C and 1040 DEG C, and strain rate is respectively 0.001s ^-1, 0.01s ^-1, 0.1s ^-1and ls ^-1, dependent variable is 1.2.

Step 2: the mathematical model setting up prediction nickel-base alloy work hardening and dynamic recovery behavior:

$\left\{\begin{array}{c}\mathrm{\σ}={\mathrm{\σ}}_y+{\mathrm{\σ}}_i\\ {\mathrm{\σ}}_y=A_y{d}_0^{m_y}{\left(\stackrel{\·}{\mathrm{\ϵ}}\exp (Q_y/\mathrm{RT})\right)}^{n_y}\\ {\mathrm{\σ}}_i=\mathrm{M\α\μb}\sqrt{{\mathrm{\ρ}}_i}\\ {\stackrel{\·}{\mathrm{\ρ}}}_i=M(\sqrt{{\mathrm{\ρ}}_i}/k_w+1/d_0)\stackrel{\·}{\mathrm{\ϵ}}/b-f_v{\mathrm{\ρ}}_i\stackrel{\·}{\mathrm{\ϵ}}\\ k_w=A_w{d}_0^{m_w}{\left(\stackrel{\·}{\mathrm{\ϵ}}\exp (Q_w/\mathrm{RT})\right)}^{n_w}\\ f_v=A_v{d}_0^{m_v}{\left(\stackrel{\·}{\mathrm{\ϵ}}\exp (Q_v/\mathrm{RT})\right)}^{n_v}\end{array}\right.$

Wherein σ _yfor yield stress, σ _tfor dislocation desity develops the stress caused; R is unified gas law constant (8.314Jmol ^-1k ^-1); M is Taylor coefficients, equals 3.06; α is dislocation interactions constant, equals 0.3; μ is material modulus of shearing, with temperature significant correlation, can be expressed as μ=86.94-0.027T with the relation of temperature T; B is Bai Shi vector (2.54 × 10 ^-10m); ρ _ifor dislocation desity, original state dislocation desity is assumed to 1 × 10 ¹¹m ^-2; for dislocation desity develops speed; k _wand f _vbe respectively strain hardening coefficient and dynamic recovery coefficient; A _y, A _w, A _v, m _y, m _w, m _v, n _y, n _w, n _v, Q _y, Q _wand Q _vbe material parameter;

Step 3: the true stress-true strain data of the GH4169 alloy utilizing high temperature compressed experiment to obtain, can record the yield stress of GH4169 alloy by 0.2% strain compensation method.According to the true stress-true strain data of GH4169 alloy, obtain its yield stress σ further _ywith alternating temperature temperature T, strain rate initial Grain Size d ₀between relation, namely ln σ _y-1/T and ln σ _y-lnd ₀graph of a relation, as shown in Figures 1 to 3.By the method for data linear fit, right ln σ _y-1/T and ln σ _y-lnd ₀data in graph of a relation return, and determine material parameter A _y, m _y, n _yand Q _yconcrete numerical value be respectively 0.708 ,-0.123,0.09 and 663.870kJ/mol.Therefore, yield stress and alternating temperature temperature T, strain rate initial Grain Size d ₀between relation can be expressed as

Utilize diff principle, by the dislocation desity increment Delta ρ caused with arbitrarily small strain increment Δ ε _ibe expressed as with stress increment Δ σ with Δ σ=(α M μ b ρ _i ^-1/2) Δ ρ _i/ 2, write iteration accumulation algorithm program, embed numerical simulation software, in conjunction with the true stress-true strain data of GH4169 alloy, be optimized and solve, determine the material parameter A predicted in the mathematical model of nickel-base alloy work hardening and dynamic recovery behavior _w, A _v, m _w, m _v, n _w, n _v, Q _wand Q _vconcrete numerical value, as shown in table 1.

The GH4169 alloy material parameter value that table 1 optimization obtains

Step 4: the prediction nickel-base alloy work hardening that the material parameter substitution step 2 that step 3 obtains is set up and the mathematical model of dynamic recovery behavior, utilize diff principle, write iteration accumulation algorithm program, embed numerical simulation software, realize the renewal of material parameter at any iteration step of Deformation Parameters and temperature distortion parameter influence, and then the work hardening of nickel-base alloy and dynamic recovery behavior under prediction random variation condition, wherein Deformation Parameters comprises deformation temperature and strain rate, and the material parameter of temperature distortion parameter influence comprises yield stress σ _y, strain hardening coefficient k _wwith dynamic recovery coefficient f _v.

Figure 4 shows that predicting the outcome of the work hardening of GH4169 alloy and dynamic recovery behavior under constant temperature constant strain rate condition.Predicting the outcome of the work hardening of GH4169 alloy and dynamic recovery behavior under deformation condition is become when Figure 5 shows that.Load path 1 is when true strain 0.2, and strain rate is from 0.01s ^-1sport 1s ^-1; Load path 2 is when true strain 0.4, and strain rate is from 1s ^-1sport 0.01s ^-1.Dotted line is strain rate 0.01s ^-1and 1s ^-1true stress-true strain curve under condition, can find at the distortion initial stage, and prediction curve overlaps with the constant temperature constant strain rate under corresponding deformation condition; After sudden change occurs, prediction curve moves closer to the constant temperature constant strain rate curve under new deformation state condition.Can find from figure, the predicted value of the true stress-true strain of GH4169 alloy and experiment value coincide good, show that method of the present invention can predict work hardening and the dynamic recovery behavior of GH4169 alloy exactly.

By reference to the accompanying drawings example of the present invention is described above; but the present invention is not limited to above-mentioned concrete embodiment, above-mentioned embodiment is only exemplary, is not circumscribed; any innovation and creation being no more than the claims in the present invention, all within protection of the present invention.

Claims (6)

1. predict the method for nickel-base alloy work hardening and dynamic recovery behavior for one kind, it is characterized in that: taken into full account the impact of real-time deformation condition on nickel-base alloy hot deformation behavior, theoretical based on dislocation desity, propose a kind of mathematical model predicting nickel-base alloy work hardening and dynamic recovery behavior, achieve the quick and precisely prediction to nickel-base alloy work hardening under random variation condition and dynamic recovery behavior, the method comprises the following steps:

Step 1: be 900 DEG C ~ 1100 DEG C and strain rate in deformation temperature be 0.0005s ^-1~ 10s ^-1thermal deformation conditions under, high temperature compressed experiment is carried out to the nickel-base alloy that Initial Grain Size is 20 μm ~ 90 μm, obtains the true stress-true strain data of nickel-base alloy;

Step 2: the mathematical model setting up prediction nickel-base alloy work hardening and dynamic recovery behavior:

$\left\{\begin{array}{c}\mathrm{\σ}={\mathrm{\σ}}_y+{\mathrm{\σ}}_i\\ {\mathrm{\σ}}_y=A_y{d}_0^{m_y}{\left(\stackrel{\·}{\mathrm{\ϵ}}\exp (Q_y/\mathrm{RT})\right)}^{n_y}\\ {\mathrm{\σ}}_i=\mathrm{M\α\μb}\sqrt{{\mathrm{\ρ}}_i}\\ {\stackrel{\·}{\mathrm{\ρ}}}_i=M(\sqrt{{\mathrm{\ρ}}_i}/k_w+1/d_0)\stackrel{\·}{\mathrm{\ϵ}}/b-f_v{\mathrm{\ρ}}_i\stackrel{\·}{\mathrm{\ϵ}}\\ k_w=A_w{d}_0^{m_w}{\left(\stackrel{\·}{\mathrm{\ϵ}}\exp (Q_w/\mathrm{RT})\right)}^{n_w}\\ f_v=A_v{d}_0^{m_v}{\left(\stackrel{\·}{\mathrm{\ϵ}}\exp (Q_v/\mathrm{RT})\right)}^{n_v}\end{array}\right.$

Wherein σ _yfor yield stress, σ _ifor the stress that dislocation desity causes, M is Taylor coefficients, and α is dislocation interactions constant, and μ is material modulus of shearing, and b is Bai Shi vector, and R is unified gas law constant, ρ _ifor dislocation desity, for dislocation desity develops speed, k _wand f _vbe respectively strain hardening coefficient and dynamic recovery coefficient; A _y, A _w, A _v, m _y, m _w, m _v, n _y, n _w, n _v, Q _y, Q _wand Q _vbe material parameter;

Step 3: according to the deformation condition of high temperature compressed experiment and the true stress-true strain data of nickel-base alloy, set up the yield stress σ of nickel-base alloy _ywith alternating temperature temperature T, strain rate initial Grain Size d ₀between relation, namely ln σ _y-1/T and ln σ _y-ln d ₀graph of a relation, and the method determination material parameter A passing through linear fit _y, m _y, n _yand Q _yconcrete numerical value;

Utilize diff principle, by the dislocation desity increment Delta ρ caused with arbitrarily small strain increment Δ ε _ibe expressed as with stress increment Δ σ with Δ σ=(α M μ b ρ _i ^-1/2) Δ ρ _i/ 2, write iteration accumulation algorithm program, embed numerical simulation software, in conjunction with the true stress-true strain data of nickel-base alloy, be optimized and solve, determine the material parameter A predicted in the mathematical model of nickel-base alloy work hardening and dynamic recovery behavior _w, A _v, m _w, m _v, n _w, n _v, Q _wand Q _vconcrete numerical value;

Step 4: the prediction nickel-base alloy work hardening that the material parameter substitution step 2 that step 3 is determined is set up and the mathematical model of dynamic recovery behavior, utilize diff principle, write iteration accumulation algorithm program, embed numerical simulation software, realize the renewal of material parameter at any iteration step of Deformation Parameters and temperature distortion parameter influence, and then the work hardening of nickel-base alloy and dynamic recovery behavior under prediction random variation condition, wherein Deformation Parameters comprises deformation temperature and strain rate, and the material parameter of temperature distortion parameter influence comprises yield stress σ _y, strain hardening coefficient k _wwith dynamic recovery coefficient f _v.

2. the method for claim 1, is characterized in that: the deformation temperature range described in step 1 is 900 DEG C ~ 1100 DEG C, and strain rate scope is 0.0005s ^-1~ 10s ^-1, the Initial Grain Size scope of nickel-base alloy is 20 μm ~ 90 μm.

3. the method for claim 1, is characterized in that: the strain hardening coefficient k described in step 2 _w, dynamic recovery coefficient f _vwith alternating temperature temperature T, strain rate initial Grain Size d ₀between relation can be expressed as with $f_v=A_v{d}_0^{m_v}{\left(\stackrel{\·}{\mathrm{\ϵ}}\exp (Q_v/\mathrm{RT})\right)}^{n_v}.$

4. the method for claim 1, is characterized in that: the yield stress σ of the nickel-base alloy described in step 3 _ywith alternating temperature temperature T, strain rate initial Grain Size d ₀between relation be by determining the method for experimental data linear fit.

5. the method for claim 1, it is characterized in that: the material parameter in the mathematical model of the prediction nickel-base alloy work hardening described in step 3 and dynamic recovery behavior utilizes diff principle, write iteration accumulation algorithm program, embed numerical simulation software, the true stress-true strain in conjunction with nickel-base alloy is data-optimized to be solved and obtains.

6. the method for claim 1, it is characterized in that: the material parameter realizing Deformation Parameters and temperature distortion parameter influence described in step 4 upgrades at any iteration step, wherein Deformation Parameters comprises deformation temperature and strain rate, and the material parameter of temperature distortion parameter influence comprises yield stress σ _y, strain hardening coefficient k _wwith dynamic recovery coefficient f _v.