基于新加工硬化率方法的AZ80鎂合金動態(tài)再結(jié)晶臨界條件

王忠堂，霍 達，于曉林

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基于新加工硬化率方法的AZ80鎂合金動態(tài)再結(jié)晶臨界條件

王忠堂1，霍 達2，于曉林1

(1. 沈陽理工大學(xué) 材料科學(xué)與工程學(xué)院，沈陽 110159；2. 東北財經(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AZ80鎂合金進行熱拉伸實驗，測試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鎂合金熱變形過程的本構(gòu)關(guān)系模型；提出一種新的加工硬化率方法，當加工硬化率函數(shù)對應(yīng)變()求一階導(dǎo)數(shù)后的函數(shù)取最小值時所對應(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。模型計算結(jié)果與Sellars模型結(jié)果相吻合。

AZ80鎂合金；加工硬化率；動態(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)之間的計算模型。

1 應(yīng)力?應(yīng)變曲線

實驗材料為軋制態(tài)AZ80鎂合金板材，熱拉伸變形實驗溫度分別為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)生塑性變形時發(fā)生加工硬化的程度，數(shù)學(xué)表達式為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()值的變化過程可以分4個區(qū)域來分析，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，如圖4所示。當應(yīng)變值()小于穩(wěn)定應(yīng)變值(st)時，發(fā)生的動態(tài)再結(jié)晶為連續(xù)動態(tài)再結(jié)晶，而當應(yīng)變值()大于穩(wěn)定應(yīng)變值(st)時，加工硬化率()值在0值附近上下波動，說明發(fā)生的動態(tài)再結(jié)晶是周期型動態(tài)再結(jié)晶。顯然，在一次熱拉伸變形過程中，加工硬化率()值的變化規(guī)律是從正值降低至負值，再從負值增大到0值的過程，第一次返回至0值時的應(yīng)變值定義為穩(wěn)態(tài)應(yīng)變(st)，它所對應(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)是指材料完成動態(tài)再結(jié)晶時的應(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

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

對式(3)求導(dǎo)數(shù)，得到：

對式(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態(tài)再結(jié)晶時的臨界應(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，說明變形溫度升高有利于發(fā)生動態(tài)再結(jié)晶。從圖6(c)和(d)可以看出，應(yīng)變速率對臨界應(yīng)變和臨界應(yīng)力都產(chǎn)生無益的影響，即隨著應(yīng)變速率的升高，臨界條件也升高，這主要是因為當變形速率較高時沒有充分的時間形成再結(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鎂合金動態(tài)再結(jié)晶的臨界條件

5 動態(tài)再結(jié)晶時的穩(wěn)態(tài)應(yīng)變

根據(jù)Kopp模型[20]可以得到：

對式(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，則得到動態(tài)再結(jié)晶完成時的穩(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) 測試了AZ80鎂合金的真實應(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，即當函數(shù)()=?d/d取最小值時所對應(yīng)的應(yīng)變值即為臨界應(yīng)變(c)，與臨界應(yīng)變(c)對應(yīng)的就是臨界應(yīng)力(c)，簡化了計算過程。

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鎂合金熱變形過程中動態(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，以及動態(tài)再結(jié)晶完成時的穩(wěn)態(tài)應(yīng)變(st)與參數(shù)的關(guān)系模型。

[1] 權(quán)國政, 趙 磊, 王 陽, 石 彧, 周 杰. 基于流動應(yīng)力曲線的AZ80鎂合金動態(tài)再結(jié)晶動力學(xué)表征[J]. 功能材料, 2011, 42(6): 1142?1146. QUAN Guo-zheng, ZHAO Lei, WANG Yang, SHI Yu, ZHOU Jie. A characterization for the dynamic recrystallization kinetics of AZ80 magnesium alloy based on flow curve[J]. Journal of Functional materials, 2011, 42(6): 1142?1146.

[2] 蔡 赟, 孫朝陽, 萬 李, 陽代軍, 周慶軍, 蘇澤興. AZ80 鎂合金動態(tài)再結(jié)晶軟化行為研究[J]. 金屬學(xué)報, 2016, 52(9): 1123?1132. CAI Yun, SUN Chao-yang, WAN Li, YANG Dai-jun, ZHOU Qing-jun, SU Ze-xing. Study on the dynamic recrystallization softening behavior of AZ80 magnesium alloy[J]. Acta Metallurgica Sinica, 2016, 52(9): 1123?1132.

[3] 王天一, 丁漢林, 劉育鋒, 魏 峰, 張義偉,程廣萍. Mg-1.0%Zn-1.5%Ca合金熱壓縮過程的顯微組織及動態(tài)再結(jié)晶行為[J]. 中國有色金屬學(xué)報, 2014, 24(10): 2474?2481. WANG Tian-yi, DING Han-lin, LIU Yu-feng, WEI Feng, ZHANG Yi-wei, CHENG Guang-ping. Microstructure and dynamic recrystallization behavior of Mg-1.0%Zn-1.5%Ca alloy during hot compression[J]. The Chinese Journal of Nonferrous Metals, 2014, 24(10): 2474?2481.

[4] 金朝陽, 李克嚴, 吳欣桐, 嚴 凱. 鎂合金高溫流動特性與動態(tài)再結(jié)晶的關(guān)聯(lián)機制[J]. 揚州大學(xué)學(xué)報(自然科學(xué)版), 2015, 18(3): 41?45. JIN Chao-yang, LI Ke-yan, WU Xin-tong, YAN Kai. Correlation between dynamic recrystallization and flow characteristics of high temperature magnesium alloys[J]. Journal of Yangzhou University(Natural Science Edition), 2015, 18(3): 41?45.

[5] 童小山, 彭 建, 石大偉, 潘復(fù)生, 彭 毅. ZM21及ZM61合金的熱變形行為與動態(tài)再結(jié)晶臨界條件的表征[J]. 中國有色金屬學(xué)報, 2013, 23(8): 2069?2075. TONG Xiao-shan, PENG Jian, SHI Da-wei, PAN Fu-sheng, PENG Yi. Thermal compression behavior and characterization of dynamic recrystallization critical conditions for ZM21 and ZM61 magnesium alloys[J]. The Chinese Journal of Nonferrous Metals, 2013, 23(8): 2069?2075.

[6] LIU Zhi-yi, HUANG Tian-tian, LIU Wen-juan, KANG Sukbong. Dislocation mechanism for dynamic recrystallization in twin-roll casting Mg–5.51Zn–0.49Zr magnesium alloy during hot compression at different strain rates[J]. Transactions of Nonferrous Metals Society of China, 2016, 26(2): 378?389.

[7] 劉 筱, 朱必武, 李落星, 唐昌平. 擠壓態(tài)AZ31鎂合金熱變形過程中的孿生和織構(gòu)演變[J]. 中國有色金屬學(xué)報, 2016, 26(2): 288?296. LIU Xiao, ZHU Bi-wu, LI Luo-xing, TANG Chang-ping. Twinning and texture evolution in extruded AZ31 magnesium alloy during hot deformation[J]. The Chinese Journal of Nonferrous Metals, 2016, 26(2): 288?296.

[8] 婁 超, 張喜燕, 任 毅. 動態(tài)塑性變形下AZ31鎂合金的孿生特征[J]. 中國有色金屬學(xué)報, 2015, 25(10): 2642?2649. LOU Chao, ZHANG Xi-yan, REN Yi. Twinning characteristic of AZ31 magnesium alloy during dynamic plastic deformation[J]. The Chinese Journal of Nonferrous Metals, 2015, 25(10): 2642?2649.

[9] SHAO Yi-chuan, TANG Tao, LI Da-yong, ZHOU Guo-wei, ZHANG Shao-rui, PENG Ying-hong. Polycrystal modeling of hot extrusion texture of AZ80 magnesium alloy[J]. Transactions of Nonferrous Metals Society of China, 2016, 26(4): 1063?1072.

[10] WANG Zhi-qiang, CHAPUIS A, LIU Qing. Simulation of mechanical behavior of AZ31 magnesium alloy during twin-dominated large plastic deformation[J]. Transactions of Nonferrous Metals Society of China, 2015, 25(11): 3595?3603.

[11] LI Ling, MURáNSKY O, FLORES-JOHNSON E A, KABRA Saurabh, SHEN Lu-ming, PROUST Gwéna?lle. Effects of strain rate on the microstructure evolution and mechanical response of magnesium alloy AZ31[J]. Materials Science and Engineering A, 2017, 684: 37?46.

[12] CHEN Gao-jin, CHEN Liang, ZHAO Guo-qun, ZHANG Cun-sheng, CUI Wei-chao. Microstructure analysis of an Al-Zn-Mg alloy during porthole die extrusion based on modeling of constitutive equation and dynamic recrystallization[J]. Journal of Alloys and Compounds, 2017, 710: 80?91.

[13] SELLARS C M, WHITEMAN J A. Recrystallization and grain growth in hot rolling[J]. Metal Science, 1979, 13(3): 187?194.

[14] RYAN N D, KOCKS U F. A review of the stages of work hardening[J]. Solid State Phenomena, 1993, 35(36): 1?18.

[15] POLIAK E I, JONAS J J. A one-parameter approach to determining the critical conditions for the initiation of dynamic recrystallization[J]. Acta Materialia, 1996, 44(1): 127?136.

[16] NAJAFIZADEH A, JONAS J J. Predicting the critical stress for initiation of dynamic recrystallization[J]. ISIJ International, 2006, 46(11): 1679?1684.

[17] 歐陽德來, 魯世強, 崔 霞. 應(yīng)用加工硬化率研究TA15鈦合金區(qū)變形的動態(tài)再結(jié)晶臨界條件[J]. 航空材料學(xué)報, 2010, 30(2): 17?23. OUYANG De-lai, LU Shi-qiang, CUI Xia. Study on critical strains of dynamic recrystallization during β process in TA15 titanium alloy using working hardening rate[J]. Journal of Aeronautical Materials, 2010, 30(2): 17?23.

[18] 王忠堂, 鄧永剛, 張士宏. 基于加工硬化率的高溫合金IN690動態(tài)再結(jié)晶臨界條件[J]. 材料熱處理學(xué)報, 2014, 35(7): 193?197. WANG Zhong-tang, DENG Yong-gang, ZHANG Shi-hong. Critical conditions of dynamic recrystallization for super-alloy IN690 based on hardening rate[J]. Transactions of Materials and Heat Treatment, 2014, 35(7): 193?197.

[19] SELLARS C M, MCTEGART W J. On the mechanism of hot deformation[J]. ACTA Metallurgica, 1966, 14: 1136?1138.

[20] KARHAUSEN K, KOPP R. Model for intergrated process microstructure simulation in hot forming[J]. Steel Research, 1992, 63: 247?266.

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

國家自然科學(xué)基金資助項目(51575366)；遼寧省教育廳資助項目(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)