結(jié)構(gòu)消(耗)能元件芯材SN490B本構(gòu)關(guān)系數(shù)值模擬

結(jié)構(gòu)消(耗)能元件芯材SN490B本構(gòu)關(guān)系數(shù)值模擬

柳曉晨1，2，王元清1，戴國(guó)欣2，王佼姣1，石永久1

(1. 清華大學(xué) 土木工程安全與耐久教育部重點(diǎn)實(shí)驗(yàn)室，土木工程系，北京100084;

2. 重慶大學(xué) 山地城鎮(zhèn)建設(shè)與新技術(shù)教育部重點(diǎn)實(shí)驗(yàn)室，土木工程學(xué)院，重慶400045)

摘要：采用消(耗)能元件的結(jié)構(gòu)在遭受地震作用時(shí)，元件芯材首先屈服進(jìn)入塑性階段，利用其滯回變形消耗地震輸入能量，保護(hù)主體結(jié)構(gòu)，元件芯材本構(gòu)關(guān)系的數(shù)值模擬是對(duì)采用消(耗)能元件結(jié)構(gòu)進(jìn)行抗震分析與設(shè)計(jì)的基礎(chǔ)。為更真實(shí)地模擬結(jié)構(gòu)消(耗)能元件芯材在單調(diào)和循環(huán)荷載下的本構(gòu)響應(yīng)，更準(zhǔn)確地對(duì)采用消(耗)能元件結(jié)構(gòu)進(jìn)行結(jié)構(gòu)彈塑性地震響應(yīng)分析，對(duì)常用作消(耗)能元件芯材的日本高延性鋼材SN490B的單調(diào)、循環(huán)加載本構(gòu)及循環(huán)骨架曲線進(jìn)行了數(shù)值模擬，包括：采用Esmaeily-Xiao二次流塑性模型模擬材料在單調(diào)荷載作用下彈性段、屈服段、強(qiáng)化段和二次流塑段4個(gè)階段；采用混合強(qiáng)化模型模擬材料循環(huán)荷載作用下的本構(gòu)響應(yīng)，運(yùn)用大型通用有限元軟件ABAQUS結(jié)合數(shù)值模擬參數(shù)對(duì)16種不同循環(huán)加載制度下的循環(huán)加載試驗(yàn)進(jìn)行模擬，并與試驗(yàn)結(jié)果進(jìn)行對(duì)比；采用Ramberg-Osgood模型、無(wú)量綱化的Ramberg-Osgood模型及兩段式模型模擬循環(huán)骨架曲線。研究結(jié)果表明：所采用數(shù)學(xué)模型可以較好地模擬SN490B鋼材單調(diào)、循環(huán)加載本構(gòu)響應(yīng)及循環(huán)骨架曲線，數(shù)值模擬與試驗(yàn)結(jié)果擬合較好。

關(guān)鍵詞：SN490B；本構(gòu)模擬；循環(huán)加載；滯回性能；有限元分析

Received:2015-03-24

Foundation item：National Natural Science Foundation of China(No.51038006)

地震造成的災(zāi)害首先是建筑物的破壞，耗能減震技術(shù)通過(guò)在結(jié)構(gòu)中布置消(耗)能元件，當(dāng)?shù)卣鹱饔脮r(shí)，消(耗)能元件作為犧牲構(gòu)件首先屈服進(jìn)入塑性階段，通過(guò)滯回耗能，改變能量在結(jié)構(gòu)中的分配，避免結(jié)構(gòu)主體和主要受力構(gòu)件吸收過(guò)多的地震能量而出現(xiàn)嚴(yán)重破壞，實(shí)現(xiàn)對(duì)結(jié)構(gòu)的保護(hù)。消(耗)能元件性能主要取決于用于滯回耗能的元件芯材性能。通常用作元件芯材的鋼材主要有低屈服點(diǎn)鋼材及高延性鋼材，如日本SN系列鋼材、LY系列鋼材、中國(guó)的BLY系列鋼材及部分碳素結(jié)構(gòu)鋼[1-4]。

針對(duì)用作消(耗)能元件芯材鋼材的研究主要集中于鋼材的制造工藝參數(shù)[5-8]、拉伸性能[6、9-12]、滯回性能及低周疲勞性能[12-16]，對(duì)本構(gòu)關(guān)系的數(shù)值模擬研究較少。因此，筆者采用不同的數(shù)學(xué)模型對(duì)常用作消(耗)能元件芯材的日本高延性鋼材SN490B的單調(diào)、循環(huán)加載本構(gòu)響應(yīng)及循環(huán)骨架曲線進(jìn)行了數(shù)值模擬，并運(yùn)用大型通用有限元軟件ABAQUS結(jié)合數(shù)值模擬參數(shù)模擬16種不同循環(huán)加載制度下的循環(huán)加載試驗(yàn)，與試驗(yàn)結(jié)果進(jìn)行對(duì)比，為采用消(耗)能元件的實(shí)際工程抗震分析與設(shè)計(jì)提供借鑒。

1單調(diào)加載本構(gòu)關(guān)系數(shù)值模擬

通過(guò)調(diào)節(jié)K1、K2、K3、K4四個(gè)參數(shù)模擬不同種鋼材的力學(xué)性能，其數(shù)學(xué)表達(dá)式如式(1)。

(1)

式中：Es為鋼材彈性模量、fy為屈服應(yīng)力、K1為材料強(qiáng)化段起始應(yīng)變與屈服應(yīng)變之比、K2為峰值點(diǎn)應(yīng)變與屈服應(yīng)變之比、K3為極限應(yīng)變與屈服應(yīng)變之比，K4為峰值應(yīng)力與屈服應(yīng)力之比。

圖1　簡(jiǎn)化后的二次塑流模型Fig.1　The simplified secondary flow plasticity

根據(jù)王元清等[4]對(duì)SN490B鋼材的材性試驗(yàn)數(shù)據(jù)運(yùn)用Origin8.5自定義曲線功能進(jìn)行擬合，整理計(jì)算所得模型各參數(shù)如表1所示。

表1　單調(diào)加載二次塑流模型參數(shù)

圖2　單調(diào)加載試驗(yàn)與數(shù)值模擬對(duì)比曲線Fig.2　Comparison of experimental curves undermonotonic load with the

2循環(huán)加載本構(gòu)關(guān)系數(shù)值模擬

2.1　數(shù)值模型

采用大型通用有限元軟件ABAQUS對(duì)SN490B鋼材循環(huán)加載本構(gòu)響應(yīng)進(jìn)行數(shù)值模擬，從彈性、塑性?xún)蓚€(gè)方面定義材料屬性參數(shù)。

材料的彈性屬性由楊氏彈性模量E和泊松比μ確定。泊松比μ取0.3，彈性模量E根據(jù)表1的試驗(yàn)數(shù)據(jù)取為198 900 N/mm2。

材料在循環(huán)荷載作用下的塑性屬性采用混合強(qiáng)化模型模擬，混合強(qiáng)化模型由各向同性強(qiáng)化和隨動(dòng)強(qiáng)化兩部分構(gòu)成[18]。描述材料在循環(huán)荷載作用下料塑性屬性的參數(shù)有：等效塑性應(yīng)變?yōu)榱銜r(shí)的屈服面等效應(yīng)力(即材料的屈服強(qiáng)度)ó|0、隨動(dòng)強(qiáng)化參數(shù)初值Ck、隨動(dòng)強(qiáng)化參數(shù)減小比率γk、屈服面最大變化值Q∞以及硬化參數(shù)b。

圖3　對(duì)稱(chēng)應(yīng)變循環(huán)試驗(yàn)曲線Fig.3　Stress-strain curves under cyclic symmetric strain

(2)

(3)

(4)

表2　循環(huán)強(qiáng)化參數(shù)

(5)

(6)

(7)

圖4　穩(wěn)定循環(huán)曲線Fig.4　Stress-strain curves under steady cyclic

采用上述方法對(duì)王元清等[4]對(duì)SN490B鋼材材性試驗(yàn)加載制度為H7、H8的試驗(yàn)數(shù)據(jù)進(jìn)行處理，并運(yùn)用Origin8.5自定義曲線功能進(jìn)行擬合，校對(duì)和調(diào)整后得ABAQUS中cycle hardening中的材料參數(shù)如表2所示，運(yùn)用表2中參數(shù)定義材料屬性，對(duì)試驗(yàn)進(jìn)行數(shù)值模擬，數(shù)值曲線與試驗(yàn)數(shù)據(jù)曲線對(duì)比如圖7(e)、(f)所示，擬合效果較好。

2.2　有限元模擬

王元清等[4]針對(duì)SN490B鋼材的循環(huán)加載試驗(yàn)試件尺寸如圖5所示，試件由固定段、過(guò)渡段和試驗(yàn)段3部分構(gòu)成。在ABAQUS中建立試驗(yàn)段模型即15 mm×15 mm×20 mm的長(zhǎng)方體，單元類(lèi)型采用8節(jié)點(diǎn)六面體線性減縮積分單元C3D8R，指定參考點(diǎn)RP(20,7.5,7.5)，并將參考點(diǎn)與實(shí)體相關(guān)聯(lián)。

圖5　SN490B試件尺寸圖Fig.5　dimension figure of SN490B

采用表2中的參數(shù)分別定義ABAQUS材料屬性模塊中 Elastic、Plastic和cyclic hardening部分的材料屬性參數(shù)。在Load功能模塊定義邊界條件和位移加載過(guò)程：將試驗(yàn)段的一端視為固定端Set-1-fixed，另一端進(jìn)行位移加載Set-2-RP，在Tools-Amplitude-manager中根據(jù)圖7所示試驗(yàn)實(shí)際加載情況定義加載制度。在Job功能模塊中提交分析。

2.3　有限元模擬結(jié)果

將分析結(jié)果繪成應(yīng)力應(yīng)變曲線，并與圖6所示16種循環(huán)加載制度下實(shí)際試驗(yàn)數(shù)據(jù)繪成的應(yīng)力應(yīng)變曲線進(jìn)行比較，比較結(jié)果如圖7所示。

圖6　試件編號(hào)及加載制度Fig6　Specimen number and cyclic loading

圖7　有限元模擬試驗(yàn)結(jié)果與實(shí)際試驗(yàn)結(jié)果應(yīng)-力應(yīng)變曲線對(duì)比Fig.7　Comparative stress-strain curves of finite element analysis results and experimental results

2.4　循環(huán)加載骨架曲線數(shù)值模擬

當(dāng)后續(xù)編程開(kāi)發(fā)SN490B材料在單調(diào)和循環(huán)荷載作用下的滯回規(guī)則以形成完整的本構(gòu)模型用于地震作用結(jié)構(gòu)反應(yīng)計(jì)算、提高計(jì)算效率時(shí)，材料首次加載按照已經(jīng)驗(yàn)證過(guò)的簡(jiǎn)化后的二次塑流模型，卸載按彈性直線卸載，再次加載，應(yīng)力應(yīng)變關(guān)系過(guò)屈服點(diǎn)后，沿骨架曲線前進(jìn)，本文采用式(8)所示變形形式Ramberg-Osgood方程[18]對(duì)4種以ε=0為中心對(duì)稱(chēng)循環(huán)加載的骨架曲線進(jìn)行擬合。為簡(jiǎn)化計(jì)算，將式(9)帶入式(8)進(jìn)行無(wú)量綱化處理得式(10)，再對(duì)骨架曲線進(jìn)行擬合。

(8)

(9)

(10)

表3　循環(huán)骨架曲線擬合參數(shù)

為便于編程及滯回準(zhǔn)則的實(shí)現(xiàn)，骨架曲線需包含屈服點(diǎn)，因此,進(jìn)一步采用文獻(xiàn)[2]提出的兩段式模型對(duì)循環(huán)骨架曲線進(jìn)行擬合，擬合后的骨架曲線分為彈性階段和循環(huán)強(qiáng)化階段，具體表達(dá)形式如式(11)。

(11)

圖8　循環(huán)骨架曲線試驗(yàn)與數(shù)值模擬對(duì)比曲線Fig8　Comparative analysis of experimental results and cyclic skeleton curves using Ramberg-Osgood model

3結(jié)論

通過(guò)對(duì)常用作消(耗)能元件芯材的日本高延性鋼材SN490B的單調(diào)、循環(huán)加載本構(gòu)響應(yīng)及循環(huán)骨架曲線的數(shù)值模擬及運(yùn)用有限元軟件ABAQUS對(duì)16種不同循環(huán)加載制度下的循環(huán)加載試驗(yàn)的模擬可得以下結(jié)論：

1)簡(jiǎn)化后的二次塑流模型Esmaeily-Xiao模型可以較好的模擬材料在單調(diào)荷載作用下的4個(gè)階段：彈性段、屈服段、強(qiáng)化段和二次塑流段。

2)采用隨動(dòng)強(qiáng)化模型模擬材料在循環(huán)荷載作用下的響應(yīng)所得擬合參數(shù)，運(yùn)用大型通用有限元軟件ABAQUS對(duì)16種不同循環(huán)加載制度下的循環(huán)加載試驗(yàn)的模擬效果較好，適用于工程實(shí)際。

3)無(wú)量綱化前后的Ramberg-Osgood方程可以較好地?cái)M合循環(huán)骨架曲線，兩段式模型擬合后的骨架曲線分為彈性階段和循環(huán)強(qiáng)化階段，并包含屈服點(diǎn)，便于后續(xù)編程及滯回準(zhǔn)則的實(shí)現(xiàn)。

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(編輯王秀玲)

Author brief：Liu Xiaochen(1990-)，main research interest: steel structure，(E-mail)lxc2013210127@163.com.

Numerical simulation of constitutive relation of core material SN490B used in energy dissipation device

Liu Xiaochen1,2, Wang Yuanqing1, Dai Guoxin2, Wang Jiaojiao1, Shi Yongjiu1

(1. Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry； Department of Civil

Engineering, Tsinghua University, Beijing 100084, P.R. China;2. Key Laboratory of New Technology for Construction

of Cities on Mountain Area;School of Civil Engineering, Chongqing University, Chongqing 400045,P.R. China)

Abstract:When structure using energy dissipating device suffers from earthquake, its core materials will first go into the plastic yield stage and consume earthquake input energy by hysteretic deformation to protect the main structure. Therefore, the numerical simulation of core materials constitutive relation is the basis of seismic analysis and design with dissipation device. Theconstitutive relation of energy dissipation device under monotonic loading and cyclic loading elastic-plastic seismic response of the structure with energy dissipation device were investigated in the numerical simulation of monotonic constitutive relation, cyclic constitutive relation and skeleton curve of SN490B steel. The simulations include the four stages which are elastic stage, collapse stage, strain-hardening stage and secondary flow plastic stage of core material using Esmaeily-Xiao secondary flow plasticity model; the constitutive response of core materials under cyclic loading using combined hardening; the skeleton curve using the Ramberg-Osgood model, dimensionless Ramberg-Osgood skeleton curve model and double-linear model. Based on finite element software ABAQUS combined with numerical simulation parameters, numerical simulation of 16 different cyclic loading tests was conducted and compared with the test results. The results show that: mathematical model can be used to simulate the monotonic constitutive response, cyclic constitutive response and cyclic skeleton curve of SN490B steel accurately. Numerical simulation and experimental results fit well.

Key words:SN490B;constitutive relations;cyclic loading;hysteretic behavior;CAE

作者簡(jiǎn)介：柳曉晨(1990-)，女，主要從事鋼結(jié)構(gòu)研究,(E-mail)lxc2013210127@163.com。

基金項(xiàng)目：國(guó)家自然科學(xué)基金(51038006)

收稿日期：2015-03-24

中圖分類(lèi)號(hào)：TU511.38；TU502.6

文獻(xiàn)標(biāo)志碼：A

文章編號(hào)：1674-4764(2015)06-0070-08

doi:10.11835/j.issn.1674-4764.2015.06.010