王忠堂，霍 達(dá)，于曉林

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基于新加工硬化率方法的AZ80鎂合金動(dòng)態(tài)再結(jié)晶臨界條件

王忠堂1，霍 達(dá)2，于曉林1

(1. 沈陽(yáng)理工大學(xué) 材料科學(xué)與工程學(xué)院，沈陽(yáng) 110159；2. 東北財(cái)經(jīng)大學(xué) 金融學(xué)院，大連 116025)

在變形溫度為260~410 ℃、應(yīng)變速率為0.001~10 s?1條件下，對(duì)AZ80鎂合金進(jìn)行熱拉伸實(shí)驗(yàn)，測(cè)試AZ80鎂合金的真應(yīng)力?真應(yīng)變曲線；依據(jù)Arrhenius本構(gòu)方程形式，確定AZ80鎂合金熱變形過(guò)程的本構(gòu)關(guān)系模型；提出一種新的加工硬化率方法，當(dāng)加工硬化率函數(shù)對(duì)應(yīng)變()求一階導(dǎo)數(shù)后的函數(shù)取最小值時(shí)所對(duì)應(yīng)的應(yīng)變值，即為臨界應(yīng)變(c)。采用新的加工硬化率方法，確定AZ80鎂合金在不同變形條件下動(dòng)態(tài)再結(jié)晶的臨界應(yīng)變和臨界應(yīng)力；研究熱變形工藝參數(shù)對(duì)臨界應(yīng)變和臨界應(yīng)力的影響規(guī)律；確定AZ80鎂合金熱變形過(guò)程中的臨界應(yīng)變、臨界應(yīng)力、穩(wěn)定應(yīng)變與參數(shù)的關(guān)系模型。模型計(jì)算結(jié)果與Sellars模型結(jié)果相吻合。

AZ80鎂合金；加工硬化率；動(dòng)態(tài)再結(jié)晶；臨界條件

本文作者采用加工硬化率方法，研究AZ80鎂合金發(fā)生動(dòng)態(tài)再結(jié)晶臨界條件，確定臨界應(yīng)變、臨界應(yīng)力和穩(wěn)態(tài)應(yīng)變與參數(shù)之間的計(jì)算模型。

1 應(yīng)力?應(yīng)變曲線

實(shí)驗(yàn)材料為軋制態(tài)AZ80鎂合金板材，熱拉伸變形實(shí)驗(yàn)溫度分別為260、310、360、410 ℃；應(yīng)變速率分別為0.001、0.01、0.1、1、10 s?1。不同變形條件下的真應(yīng)力?真應(yīng)變曲線，如圖1所示。

圖1 AZ80鎂合金的真應(yīng)力?真應(yīng)變 曲線

2 本構(gòu)方程

SELLARS等[19]提出了一個(gè)雙曲正弦的材料應(yīng)力?應(yīng)變本構(gòu)方程，其中包括變形激活能、變形溫度、應(yīng)變速率等參量，見式(1)：

3 新加工硬化率方法定義

加工硬化率()的定義為材料發(fā)生塑性變形時(shí)發(fā)生加工硬化的程度，數(shù)學(xué)表達(dá)式為dd。圖3所示為材料應(yīng)力?應(yīng)變曲線上不同區(qū)域所對(duì)應(yīng)的加工硬化率變化規(guī)律。從圖3可以看出，隨著應(yīng)變()值的增大，加工硬化率()值的變化過(guò)程可以分4個(gè)區(qū)域來(lái)分析，在Ⅰ區(qū)，加工硬化率值大于零，逐漸降低；在Ⅱ區(qū)，加工硬化率值小于零，且逐漸降低；在Ⅲ區(qū)，加工硬化率值小于零，且逐漸增大；在Ⅳ區(qū)，加工硬化率值趨于穩(wěn)定在0值，且在0值附近波動(dòng)，如圖4所示。當(dāng)應(yīng)變值()小于穩(wěn)定應(yīng)變值(st)時(shí)，發(fā)生的動(dòng)態(tài)再結(jié)晶為連續(xù)動(dòng)態(tài)再結(jié)晶，而當(dāng)應(yīng)變值()大于穩(wěn)定應(yīng)變值(st)時(shí)，加工硬化率()值在0值附近上下波動(dòng)，說(shuō)明發(fā)生的動(dòng)態(tài)再結(jié)晶是周期型動(dòng)態(tài)再結(jié)晶。顯然，在一次熱拉伸變形過(guò)程中，加工硬化率()值的變化規(guī)律是從正值降低至負(fù)值，再?gòu)呢?fù)值增大到0值的過(guò)程，第一次返回至0值時(shí)的應(yīng)變值定義為穩(wěn)態(tài)應(yīng)變(st)，它所對(duì)應(yīng)的應(yīng)力?應(yīng)變曲線上的應(yīng)力值即為穩(wěn)態(tài)應(yīng)力(st)。穩(wěn)態(tài)應(yīng)變(st)是指材料完成動(dòng)態(tài)再結(jié)晶時(shí)的應(yīng)變值，如圖3所示。

圖2 峰值應(yīng)力與應(yīng)變速率和變形溫度的關(guān)系

圖3 不同階段的加工硬化率

圖4 加工硬化率的變化曲線

4 臨界條件的確定

對(duì)圖5(b)的應(yīng)力?應(yīng)變曲線進(jìn)行非線性擬合，得到擬合方程，見式(3)：

對(duì)式(3)求導(dǎo)數(shù)，得到：

對(duì)式(4)求導(dǎo)數(shù)，得到式(5)：

根據(jù)以上的分析方法，可以得到AZ80鎂合金在不同條件下的動(dòng)態(tài)再結(jié)晶時(shí)的臨界應(yīng)力和臨界應(yīng)變，如圖6所示。從圖6(a)和(b)可知，AZ80 鎂合金的臨界應(yīng)變和臨界應(yīng)力隨著變形溫度的升高而降低，說(shuō)明變形溫度升高有利于發(fā)生動(dòng)態(tài)再結(jié)晶。從圖6(c)和(d)可以看出，應(yīng)變速率對(duì)臨界應(yīng)變和臨界應(yīng)力都產(chǎn)生無(wú)益的影響，即隨著應(yīng)變速率的升高，臨界條件也升高，這主要是因?yàn)楫?dāng)變形速率較高時(shí)沒有充分的時(shí)間形成再結(jié)晶的晶核，從而使再結(jié)晶發(fā)生的比較慢，所以臨界應(yīng)變滯后。

圖5 AZ80鎂合金應(yīng)力?應(yīng)變曲線和加工硬化率(T=260 ℃，應(yīng)變速率 1)

圖6 AZ80鎂合金動(dòng)態(tài)再結(jié)晶的臨界條件

5 動(dòng)態(tài)再結(jié)晶時(shí)的穩(wěn)態(tài)應(yīng)變

根據(jù)Kopp模型[20]可以得到：

對(duì)式(7)求導(dǎo)數(shù)，得到式(8)：

根據(jù)圖9的數(shù)據(jù)以及式(8)，可以得到2=0.1135，3=0.515。代入式(7)中，則得到動(dòng)態(tài)再結(jié)晶完成時(shí)的穩(wěn)態(tài)應(yīng)變模型：

圖8 不同溫度下AZ80加工硬化率(θ)與應(yīng)變關(guān)系曲線

圖9 不同溫度下穩(wěn)態(tài)應(yīng)變與Z函數(shù)之間關(guān)系()

6 結(jié)論

1) 測(cè)試了AZ80鎂合金的真實(shí)應(yīng)力?應(yīng)變曲線，依據(jù)Arrhenius本構(gòu)方程形式，確定了AZ80鎂合金變形激活能為140671J/mol，確定了AZ80鎂合金熱變形過(guò)程的本構(gòu)關(guān)系模型。

2) 提出了一種新的加工硬化率方法，即當(dāng)函數(shù)()=?d/d取最小值時(shí)所對(duì)應(yīng)的應(yīng)變值即為臨界應(yīng)變(c)，與臨界應(yīng)變(c)對(duì)應(yīng)的就是臨界應(yīng)力(c)，簡(jiǎn)化了計(jì)算過(guò)程。

3) 采用加工硬化率方法，確定了不同變形條件下的臨界應(yīng)變和臨界應(yīng)力，隨著變形溫度的提高，臨界應(yīng)變和臨界應(yīng)力值降低；隨著應(yīng)變速率的增大，臨界應(yīng)變和臨界應(yīng)力值增大。

4) 確定了AZ80鎂合金熱變形過(guò)程中動(dòng)態(tài)再結(jié)晶的臨界條件和峰值條件與參數(shù)的關(guān)系模型，以及動(dòng)態(tài)再結(jié)晶完成時(shí)的穩(wěn)態(tài)應(yīng)變(st)與參數(shù)的關(guān)系模型。

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Critical conditions of dynamic recrystallization of AZ80 magnesium alloy based on a new method of work hardening rate

WANG Zhong-tang1, HUO Da2, YU Xiao-lin1

(1. School of Materials Science and Engineering, Shenyang Ligong University, Shenyang 110159, China; 2. Dongbei University of Finance and Economics, Dalian 116025, China)

The curves of true stress?strain of AZ80 magnesium alloy are tested by thermal tensile method, which the ranges of temperature is from 260 to 410oC and strain rates is from 0.001 to 10 s?1. According to the Arrhenius equation，the constitutive model of AZ80 magnesium alloy at thermal deformation was determined. A new work hardening rate method was proposed. When the derivative of work hardening rate function takes minimum value, the corresponding strain is the critical strain(c). The work hardening rate method was used to determine the critical strain and critical stress of dynamic recrystallization under different deformation. The relation model of critical strain and critical stress and steady strain with Zener?Hollomn parameters () were established. Calculation results of the critical strain model are in good agreement with that of Sellar’s model.

AZ80 magnesium alloy; working hardening rate; dynamic recrystallization; critical condition

Project(51575366) supported by the National Natural Science Foundation of China; Project(LG201701) supported by the Education Department of Liaoning Province, China

2017-09-13;

2018-03-15

WANG Zhong-tang; Tel: +86-24-24680841, +86-13898896289; E-mail: ztwang@imr.ac.cn

國(guó)家自然科學(xué)基金資助項(xiàng)目(51575366)；遼寧省教育廳資助項(xiàng)目(LG201701)

2017-09-13；

2018-03-15

王忠堂，教授；電話：024-24680841，13898896289；E-mail: ztwang@imr.ac.cn

10.19476/j.ysxb.1004.0609.2018.10.03

1004-0609(2018)-10-1972-08

TG146.2

A

(編輯 龍懷中)