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夾具的約束位置和間距對(duì)焊接變形的影響 重點(diǎn) 通過實(shí)驗(yàn)和仿真還原夾具約束角的變形。 兩種夾具約束對(duì)焊接變形的定量研究。 探討夾具位置和間距和焊接變形之間的關(guān)系。 摘要： 通過實(shí)驗(yàn)研究在方形板堆焊非約束自由狀態(tài)和一個(gè)夾具約束條件下焊接變形研究夾具對(duì)焊接變形的約束作用。用三維熱彈塑性有限元程序來模擬在焊接中的瞬態(tài)溫度和變形?？梢钥闯龊附咏亲冃未蟠蠼档土藠A具約束，并且仿真和實(shí)驗(yàn)之間非常相似。三方向夾具約束和正常的方向夾具約束是實(shí)際工程中典型的約束類型。兩個(gè)參數(shù)a和b，它們代表在焊接方向上的兩個(gè)夾具和從熔接線的距離之間的間距，分別聚焦。詳細(xì)討論了夾具約束對(duì)縱向收縮，橫向收縮和角變形的影響。 關(guān)鍵詞：焊接變形；夾具約束位置；約束間距；測(cè)量；FEM 1.簡介 焊接過程中通常產(chǎn)生變形和殘余應(yīng)力，是工程意外的結(jié)果。焊接變形劣化結(jié)構(gòu)的尺寸，影響了產(chǎn)品的外觀。尤其是對(duì)外形畸變的諸如薄壁結(jié)構(gòu)容易發(fā)生角變形和扭曲變形，以及它們最終需要的的校正工作。附加過程不僅會(huì)增加生產(chǎn)周期，而且增加成本。為了降低生產(chǎn)成本，因此有必要通過一些有效的方法，以減少焊接變形。殘余應(yīng)力降低結(jié)構(gòu)中的疲勞強(qiáng)度和填充劑強(qiáng)度方面的性能。要采用適當(dāng)?shù)暮附雍鬅崽幚砘驒C(jī)械方法，以釋放殘余應(yīng)力。 McPherson在2010年發(fā)表的電弧焊接的反面線加熱可以產(chǎn)生相反的彎矩來糾正。如由Ando等在1982年描述的，使用感應(yīng)加熱技術(shù)在減少焊接殘余應(yīng)力的潛在益處。通過改變應(yīng)力分布，屈曲應(yīng)變也可以有效地緩解。Wang等人在2011年分析了證明了焊接大規(guī)模加強(qiáng)結(jié)構(gòu)的變形和屈曲失真可以通過管線加熱過程被減少。 焊接過程中的額外的加熱或冷卻是一種可以在過程中控制方法，以防止焊接變形。Mochizuki等人施加的額外的冷卻到T形圓角接頭的焊接區(qū)，并表明旋轉(zhuǎn)失真可以減少數(shù)值模擬的結(jié)果以外的約束。Guan等人1990年在橫截面溫差拉伸效應(yīng)的基礎(chǔ)上發(fā)明了一種命名為低應(yīng)力無變形（LSND）的方法。LSND經(jīng)證實(shí)是優(yōu)越在防止壓曲變形的薄板對(duì)接焊中。Guan和Zhang在1994年開發(fā)了一種動(dòng)態(tài)控制低應(yīng)力無變形（DC-LSND）的方法，作為另一種在進(jìn)程屈曲的活性控制方法。在該方法中，一個(gè)局部溫差拉伸由斑點(diǎn)散熱器與焊槍尾隨，并且縱向塑性應(yīng)變?cè)诤竺娴娜鄢赝ㄟ^動(dòng)態(tài)控制的區(qū)域來實(shí)現(xiàn)。 夾具在焊接工藝中被廣泛使用，以避免在焊接熱源的前面旋轉(zhuǎn)變形。Hajduk等人在2009年描述關(guān)于焊接夾具的機(jī)器人細(xì)胞點(diǎn)焊車身的設(shè)計(jì)基于模塊化的原則。焊接變形的控制，也有與外部約束和負(fù)荷。Park等人2012年通過改變拉伸應(yīng)力的方向和大小研究了各種拉伸狀態(tài)角變形和殘余應(yīng)力。Schenk等人在2009年研究了屈曲失真和角變形用于搭接接頭和T形角接合的夾緊效果。他們發(fā)現(xiàn)夾緊條件對(duì)殘余應(yīng)力和焊接變形的影響很大。Shateryana等人在2012年通過執(zhí)行三維有限元分析研究了在三種類型的本地馬蹄形夾具焊接變形和殘余應(yīng)力在鋁合金搭接接頭的約束效果。Ziaee等人在2009年研究了邊界條件的影響屈曲焊接薄板時(shí)的模式。人們發(fā)現(xiàn)，外部約束可以增加耐壓曲性，但不能消除屈曲。 然而，由夾緊或夾具焊接變形控制的定量研究是罕見的文獻(xiàn)。由于設(shè)計(jì)參數(shù)和焊接結(jié)構(gòu)的復(fù)雜多樣，一些約束條件的有限的實(shí)驗(yàn)結(jié)果都不足以概述約束效果。自從Ueda和Yamakawa在1971年確定了熱彈塑性有限元法焊接熱應(yīng)力，它已被廣泛應(yīng)用于研究和解決Ueda所描述的工程問題中。隨著技術(shù)在計(jì)算機(jī)輔助工程（CAE）的進(jìn)步，可以有效地執(zhí)行而無需額外成本的一系列數(shù)值實(shí)驗(yàn)時(shí)的仿真精度驗(yàn)證。 在這項(xiàng)研究中，之前被測(cè)量調(diào)查的夾具約束對(duì)焊接變形的影響，堆焊焊縫焊接兩個(gè)以非約束自由狀態(tài)測(cè)試試樣，并在制備的夾具約束條件和焊接變形一個(gè)三維坐標(biāo)測(cè)量裝置。隨后被用于對(duì)兩個(gè)試樣分別進(jìn)行的數(shù)值模擬。焊接變形通過數(shù)值模擬預(yù)測(cè)與實(shí)驗(yàn)結(jié)果進(jìn)行比較，并準(zhǔn)確驗(yàn)證模擬的有效性。 此外，為了評(píng)估夾具約束定量，夾具約束分為正常方向約束和三方向約束。共41多種約束條件下的數(shù)值模型進(jìn)行了分析。兩個(gè)參數(shù)a和b，這表示在從焊接線焊接的方向和距離的兩個(gè)夾具之間的間距，分別集中及其對(duì)焊接變形效果在進(jìn)行了細(xì)節(jié)研究。 2.實(shí)驗(yàn)研究 為了調(diào)查由夾具約束的影響，把如圖1（a）和（b）中所示非約束自由狀態(tài)的兩個(gè)樣品焊接在一起，并在夾具的約束條件下，分別用夾具約束樣品，所述夾具被固定在平臺(tái)上，并且平面偏轉(zhuǎn)是固定的。樣品的尺寸400毫米的長度400毫米的寬度和9毫米的厚度。該板的基體材料是SS400，焊絲的直徑為1.2毫米，材料是MG-50T。為了一個(gè)良好的焊接質(zhì)量在板表面上焊接線周圍的銹要在焊接之前除去。實(shí)驗(yàn)期間室溫約為20℃。 圖1待焊接標(biāo)本：（a）自由狀態(tài)（b）夾具約束狀態(tài)。 單面堆焊接用的是相同的焊接條件下（240 A，25 V，5毫米/秒），通過一個(gè)自動(dòng)MAG焊接機(jī)進(jìn)行。所述保護(hù)氣體為100％的CO?2。約束夾具在焊接結(jié)束時(shí)間約4分鐘后移除。焊接試樣分別示于圖2（a）和（b）中 圖2焊后試樣：（1）自由狀態(tài)（b）夾具約束狀態(tài)。 為了獲得焊接變形，小型鉆洞上盤。每個(gè)孔的中心被認(rèn)為是一個(gè)測(cè)量點(diǎn)。焊接前在板上測(cè)量點(diǎn)的坐標(biāo)，冷卻后進(jìn)行測(cè)定。最終那些減去初始坐標(biāo)，焊接變形就計(jì)算出來了。 使用所測(cè)量的結(jié)果的三個(gè)典型的焊接變形部件，縱向收縮，橫向收縮和角變形進(jìn)行評(píng)價(jià)。在縱向部分的縱向收縮Y= -190，-40，40，190毫米，分別進(jìn)行評(píng)價(jià)，如圖3所示的橫向收縮和角變形的橫截面，評(píng)價(jià)X??= 10，50，200，350，390毫米如圖4和圖5所示。變形值上頂表面和底表面上的測(cè)量點(diǎn)的平均值。 圖3?非約束自由狀態(tài)和夾具約束條件下縱向收縮：（a）4個(gè)縱向部分；（b）縱向收縮。 圖4非約束自由狀態(tài)和一個(gè)夾具約束條件下的橫向收縮：（1）5個(gè)橫截面；（二）橫向收縮。 圖5非約束自由狀態(tài)和一個(gè)夾具約束條件下角變形：（a）5個(gè)橫截面線；（b）角變形。 圖3清楚地表明，在焊接線附近縱向收縮比遠(yuǎn)離焊接線該值大很多。圖4和圖5顯示了橫向收縮和角變形在五個(gè)部分，分別是相對(duì)均勻的，因?yàn)槊繂挝缓附娱L度的焊接熱輸入是恒定的。在焊接線的精加工結(jié)束后，橫向收縮率下降，因?yàn)閴嚎s橫向塑性應(yīng)變?cè)谀┒说南鄬?duì)較弱的內(nèi)部約束變小。通過比較，可以確認(rèn)，如果用約束夾具夾緊焊接試樣，與非約束自由狀態(tài)下進(jìn)行比較，角變形可大大減少。對(duì)角變形的影響比夾具約束對(duì)縱向收縮和橫向收縮的影響相對(duì)較小。 3.數(shù)值模擬 在這項(xiàng)研究中，三維熱彈塑性有限元被采用來模擬焊接熱應(yīng)力和變形。約束夾具在以下的實(shí)驗(yàn)條件下進(jìn)行建模仿真。夾具和樣品之間的相互作用被認(rèn)為是通過夾具的末端固定。焊接過程中用溫度變化的材料精確地模擬熱機(jī)械性能?；w金屬和填充金屬都在數(shù)值模擬分別定義。溫度和機(jī)械分析進(jìn)行順序Murakawa等人提出的迭代子法（ISM）被用于機(jī)械分析以節(jié)省計(jì)算時(shí)間。 3.1 有限元模型 一種固體元件制劑一般需要進(jìn)行分析瞬態(tài)焊接熱應(yīng)力和應(yīng)變。密實(shí)網(wǎng)孔應(yīng)在焊接線的附近進(jìn)行以適應(yīng)周圍焊接熱源的溫度梯度。在這項(xiàng)研究中，六面體元件，其魯棒性和準(zhǔn)確性在處理塑性行為被Benzkey在1995年證實(shí)良好，用于焊接模擬。為約束焊接樣品的有限元模型示于圖6。在有限元模型中的焊接加強(qiáng)件的形狀，從實(shí)驗(yàn)觀察來確定，而寬度和高度分別為10毫米和2.2毫米。在焊接方向2mm的寬度方向和1.8毫米的厚度方向，焊縫區(qū)域中的元件的大小是5毫米。單元和節(jié)點(diǎn)的數(shù)量分別是15736，20448。夾具也仿照由實(shí)體單元考慮它的彈性約束。由于夾具的幾何形狀的復(fù)雜性，每個(gè)夾具被簡化為兩個(gè)長方體具有相同的長度和橫截面為實(shí)際夾具，和所述夾持面是大約15mm×10毫米。 圖6有限元網(wǎng)格的標(biāo)本夾具和焊接熱源區(qū)。 3.2 焊接熱的傳導(dǎo)分析 機(jī)械分析之前，進(jìn)行熱傳導(dǎo)分析，以獲得溫度履歷為固體元素的所有節(jié)點(diǎn)。焊接熱源，如由移動(dòng)體積內(nèi)均勻的熱生成率表示圖6。在熱傳導(dǎo)模擬中所用的溫度依賴性的物理性能示于圖7（a）中。焊接金屬（WM）的熱特性被假定是相同的用堿金屬（BM）。在高溫度超過1000℃時(shí)，材料的性能被認(rèn)為是相同的與那些在1000℃。環(huán)境溫度設(shè)定為20℃，傳熱系數(shù)被假定為24瓦/（米2??℃）的所有的表面上（Ueda等人2012）。 圖7 堿金屬和焊接金屬的材料性質(zhì)：（a）熱物理性質(zhì)；（b）機(jī)械性能。 在圖8中，在40秒的瞬態(tài)溫度領(lǐng)域進(jìn)行了繪制的剖視圖，從中可以看出，靠近熱源的區(qū)域具有大的溫度梯度，而其后部呈相對(duì)均勻的分布。上的橫截面的最大到達(dá)溫度分布表示熔合區(qū)示于圖9。 圖8瞬時(shí)溫度分布從焊接開始40秒：（一）總體視野；（二）截面圖。 圖9在橫截面和熔合區(qū)最高達(dá)到溫度分布。 3.3 熱應(yīng)力和變形的分析 通過施加瞬時(shí)溫度，焊接熱應(yīng)力及變形計(jì)算增量為每個(gè)時(shí)間步長。堿金屬和填料金屬的機(jī)械特性示于圖7（b）中。基體金屬和填充金屬的特性是除屈服應(yīng)力相同。該材料按照各向同性硬化法及相關(guān)塑性流動(dòng)規(guī)律。對(duì)于非約束自由狀態(tài)下焊接該模型中，只有剛體運(yùn)動(dòng)在有限元模型被限制。對(duì)于夾具約束試樣，夾具的端部被約束在板法線方向（?焊接時(shí)方向）。夾具約束被焊后獲釋。相變特性（deng2009），在模擬中沒有考慮。 迭代子方法（ISM），為了節(jié)省計(jì)算時(shí)間，而不損失精度?；旧?，整個(gè)模型一個(gè)被分成兩個(gè)區(qū)域具有不同的電平的非線性，如圖10所示。在本研究中，B區(qū)溫度高于300℃。其余區(qū)域不包括整個(gè)模型A中的B區(qū)域被定義為A-B的區(qū)域。在A-B區(qū)和B區(qū)都以互動(dòng)的方式解決了，而這兩個(gè)地區(qū)之間的邊界上的不平衡力迭代計(jì)算，直到平衡感到滿意。以這種方式，迭代步驟與簡單的方案相比為整個(gè)區(qū)域總數(shù)量將大大降低。 圖10區(qū)域A，B和A-B在ISM的框架示意圖。 4.焊接變形的比較 計(jì)算出的平面位移中的分布z非約束自由狀態(tài)與夾具約束條件下方向示于?圖11，它可以很容易地觀察到，面外變形的已被夾具約束大大減少。 圖11?外的面外變形（單位：mm，變形規(guī)模：10次）：（a）免費(fèi)條件下試樣；（b）與試樣夾具。 焊接仿真和測(cè)量之間變形，在所述非約束自由狀態(tài)的比較示于圖12（a） - （b）所示。如圖中所計(jì)算的縱向收縮圖12（a）是對(duì)稱的焊接線由于模型的對(duì)稱性。板的邊緣附近的縱向的收縮遠(yuǎn)小于其靠近焊接線。 圖12?焊接在非約束自由狀態(tài)變形和實(shí)驗(yàn)和模擬之間的比較：（a）縱向收縮；（b）橫向收縮；（c）角變形。 從所計(jì)算的和測(cè)量的結(jié)果，可以發(fā)現(xiàn)，在橫向收縮，在板的中間部分比邊緣附近較大，如圖12（b）中所示。最小值出現(xiàn)在焊接的精加工結(jié)束。角變形變化不大，在所有五個(gè)橫截面，如圖12（c）所示。如果在詳細(xì)的觀察，在焊接線的終端附近的橫截面的角變形比焊接線的起始端附近大。這是因?yàn)閺囊苿?dòng)焊接熱源的預(yù)熱效果強(qiáng)附近的熔接線和預(yù)角變形的終端已經(jīng)在焊接熱源的前面產(chǎn)生。所計(jì)算的縱向收縮，橫向收縮和角變形非常接近的實(shí)驗(yàn)值。 對(duì)于夾具的約束條件下的樣品，實(shí)驗(yàn)和仿真之間的角變形的結(jié)果進(jìn)行了比較，圖12所示。無論是實(shí)驗(yàn)和仿真結(jié)果表明，在角變形減少約70％，如果使用約束夾具。 圖13測(cè)量和計(jì)算焊接角變形用夾具的約束。 5.夾具約束的參數(shù)研究 5.1 的夾具約束條件模型 如果夾具通過接觸來限制板，位移僅在接觸的法線方向朝向板和夾具之間可以被假定為被約束。如果在板被焊接時(shí)被夾具牢固地固定，在夾具約束位置的位移可以被假定為完全固定在三個(gè)方向。在這項(xiàng)研究中，兩種類型的約束，簡單地命名為正常方向夾具約束和三方向夾具約束，并且在示意性圖14示出。 圖14?夾具的配置和兩種夾具約束。 在法線方向夾具約束的建模中，頂部和底部表面的距離上的節(jié)點(diǎn)B遠(yuǎn)離焊接線，表示夾具約束位置，僅在法線方向固定。在節(jié)點(diǎn)20毫米遠(yuǎn)離焊接線附加約束是用來支撐基座上板的底部表面進(jìn)行建模。 在這三個(gè)方向的夾具約束條件，夾具在其中的位移分別設(shè)置節(jié)點(diǎn)，被固定在三個(gè)方向。在所有的情況下，在節(jié)點(diǎn)處的夾具約束是從焊接的開始施加并且當(dāng)焊接結(jié)束后220 s釋放。 對(duì)于堆焊焊接模型，進(jìn)行與尺寸模擬400毫米×400毫米×10毫米。夾具被對(duì)稱地布置在焊接線的兩側(cè)。為簡單起見，該約束被直接施加在頂表面和底表面的每個(gè)夾具的節(jié)點(diǎn)上。調(diào)查夾具位置和音調(diào)上焊接變形的影響，41例的數(shù)值模擬的示于表1，包括一個(gè)非約束自由狀態(tài)下案件。 約束類型 夾具位置B（毫米） 夾具間距一（毫米） 占總病例 非限制自由狀態(tài) 無 無 1 法線方向夾具約束 30，50，100，200 5，20，40，80，200 20 三方向夾具約束 30，50，100，200 5，20，40，80，200 20 表1數(shù)值模擬的條件和情況下，各種夾具的約束。 焊接變形的組件，腱力?F，橫向收縮和角變形的中間橫截面進(jìn)行了調(diào)查。肌腱力的概念最初是由White等人在1980年表示在焊道的縱向的收縮率，并且它可以由下式來定義： 方程式（?1?） 分別是楊氏模量和縱向塑性應(yīng)變。 為了使比較更容易，肌腱力?F（a，b），橫向收縮率S（a，b）和角變形θ（a，b））在各種夾具約束位置b和俯仰a由方程進(jìn)行歸一化分別為?(2)，(3)和(4)。每個(gè)焊接變形成分，通過相應(yīng)的值除以（?F?0，S?0，θ?0）下的非約束自由狀態(tài)。 方程式（?2?） 方程式（?3?） 方程式（?4?） 如果?F（a，b），s（a，b），β（a，b）比1.0小，則意味著夾具約束減少焊接變形。如果它們是大于1.0，這意味著焊接變形在夾具約束條件下增加。由于縱向彎曲是相當(dāng)小的，在本研究中，在此不再表述。 5.2 法線方向夾具約束 在法線方向夾具約束的情況下，位置參數(shù)b和螺距參數(shù)影響約束夾具的肌腱力?F（a，b），所述歸一化的橫向收縮s（a，b）和歸一化的角變形θ（a，b）在圖15（a）-（c）中示出，肌腱力量和橫向收縮的效果并不明顯。這可以容易地理解的是，在正方向夾具約束沒有給出在平面內(nèi)的塑性應(yīng)變尤其直接影響平均通過厚度方向的值。 圖15對(duì)焊接變形法線方向夾具約束的影響：（a）受力筋；（b）橫向收縮；（c）角變形。 可以解釋，如果正方向夾具約束施加到焊接板，附加的彎曲應(yīng)力是由正常的反作用力，如圖16所形成。在上表面的拉伸應(yīng)力可減少橫向收縮的塑性應(yīng)變的量。在底表面上，該壓應(yīng)力將引起更多的橫向收縮的塑性應(yīng)變。因此，橫向塑性應(yīng)變通過厚度的分布將變得更均勻，如圖17所示。其結(jié)果是，橫向彎曲即角變形變小。 圖16形成了垂直方向夾具約束彎曲應(yīng)力場(chǎng)。 圖17在一個(gè)非約束自由狀態(tài)和正常方向夾具約束條件對(duì)中間橫截面為試樣橫向塑性應(yīng)變分布（a=80毫米;B= 30，50毫米）：（a）橫向塑性應(yīng)變；（b）橫向塑性應(yīng)變?cè)谥醒刖€（Y??= 0）。 如果夾具被放置在靠近焊接區(qū)，即，所述夾具位置參數(shù)b為30mm螺距a是大于20毫米，角變形引起的夾具約束的減少變小。這是因?yàn)?，夾具約束位置是塑性變形區(qū)內(nèi)，如圖?17（a）所示并且由塑性應(yīng)變夾具位置以外產(chǎn)生的角變形沒有被控制。這種現(xiàn)象也通過橫向塑性應(yīng)變通過板厚分布為兩所示例圖17（b）中所示。 如圖15（c）中所示，一個(gè)小的夾具約束導(dǎo)致一個(gè)小的角變形。若間距足夠小，例如小于80毫米，節(jié)距的效果變小。在這種情況下，如果該參數(shù)為大于50毫米的角變形幾乎與夾具約束位置增加b呈線性。 5.3 三方向夾具約束 在三個(gè)方向上夾具約束的情況下，夾具約束位置的影響b和歸一化a的肌腱力?F（a，b），所述歸一化的橫向收縮s（a，b），并歸一化的角變形θ（a，b）顯示在圖18（a）-（c）中，夾具約束條件下的歸一化腱力和橫向收縮率分別變大，這是從正方向夾具約束大不相同。三個(gè)方向夾具約束條件下的角變形比那些非約束自由狀態(tài)下變化小。這種現(xiàn)象與正常的方向夾具約束條件下類似。 圖18對(duì)焊接變形三方向夾具約束條件的影響：（a）受力筋；（b）橫向收縮；（c）角變形。 肌腱力和橫向收縮的三個(gè)方向夾具約束條件下的增加，是由于在感應(yīng)焊接的縱向塑性應(yīng)變和橫向塑性應(yīng)變的增加，如圖19和圖20所示。根據(jù)夾具的約束條件，在焊接的加熱階段，主要是產(chǎn)生的大的壓縮塑性應(yīng)變。這是因?yàn)樵跓崤蛎浻蓨A具強(qiáng)約束，結(jié)果壓縮塑性應(yīng)變變大與這些非約束自由狀態(tài)下進(jìn)行比較（Murakawa等人 1996年）。 圖19?上中間截面為試樣在非約束自由狀態(tài)和三方向夾具約束條件（縱向塑性應(yīng)變一個(gè)= 20毫米，B= 50毫米）：（a）一部分的輪廓；（b）在寬度方向（分布?= 5毫米）。 圖20在一個(gè)非約束自由狀態(tài)和三方向夾具約束條件（在中間橫截面橫向塑性應(yīng)變分布一個(gè)= 20毫米，B= 50毫米）：（a）一部分的輪廓；（b）在寬度方向（分布?= 5毫米）。 6.結(jié)論 在本研究中，夾具約束對(duì)焊接變形的影響進(jìn)行了研究兩者數(shù)值模擬和實(shí)驗(yàn)測(cè)量。位置和間距參數(shù)化變更為各種約束條件。根據(jù)實(shí)驗(yàn)和計(jì)算結(jié)果，得出如下結(jié)論可以得出： （1）焊接變形的有限元計(jì)算吻合與非約束自由狀態(tài)和夾具約束條件下測(cè)得的結(jié)果。 （2）所得到的結(jié)果顯示，當(dāng)使用夾具時(shí)焊接板角變形得到有效降低。 （3）三方向夾具約束，對(duì)所有的變形部件有很大的影響。 （4）法線方向夾具約束可以有效地減少角變形與肌腱力和橫向收縮的影響。 （5）一般地，當(dāng)夾具的位置和間距值較小角變形將會(huì)減少。 15 Effect of jig constraint position and pitch on welding deformation Highlights Reduction of angular distortion by jig constraint is realized by experiment and simulation. Effect of two types of jig constraint on welding deformations is quantitatively investigated. Relationships between jig position & pitch and welding deformations are explored. Abstract Quantitative study on jig constraint effect on welding deformation was carried out. Welding deformation in a square plate with bead welding under a non-constraint free condition and a jig constraint condition was investigated by experiment. A 3D thermal elastic–plastic FEM program was employed to simulate the transient temperature and deformation occurred in the welding. It is observed that welding angular distortion has been greatly reduced by the jig constraint, and a good agreement was confirmed between simulation and experiment. Three-direction jig constraint and normal direction jig constraint were defined based on typical constraint types in practical engineering. Two parameters?a?and?b, which represent the pitch between two jigs in the welding direction and the distance from the weld line, respectively, were focused. Effect of jig constraint on longitudinal shrinkage, transverse shrinkage and angular distortion were discussed in details. Keywords:Welding deformation;?Jig constraint position;?Constraint pitch;?Measurement;?FEM 1. Introduction Welding process generally produces deformation and residual stresses which are undesired results in engineering. Welding deformation deteriorates the dimensions of structures and influences the appearance of products. Especially the out of plane distortion such as angular distortion and buckling distortion occurs easily in thin-walled structures, and their correcting work is eventually needed. The additional processes will increase not only the production period but also the cost. To reduce the production cost, it is necessary to minimize the welding deformation by some efficient ways. Residual stress degrades the performance of structure in aspects of fatigue strength and bulking strength. Proper post welding heat treatment or mechanical method has to be employed in order to release the residual stresses. Line heating on the reverse side of welding arc can produce an opposite bending moment to correct angular distortion which was reported by?McPherson (2010). As described by?Ando et al. (1982), the use of an induction heating technique has potential benefit in reducing welding residual stress. By altering the stress distribution, buckling distortion can also be mitigated effectively.?Wang et al. (2011)?analyzed welding deformation of a large-scale stiffened structure and proved that buckling distortion can be reduced by line heating process. Additional heating or cooling during welding can be one of the in-process control methods to prevent welding deformation.?Mochizuki et al. (2006)?applied the additional cooling to the weld zone of a T-shape fillet joint and demonstrated that the rotational distortion can be reduced without tacking and external constraint based on the results of numerical simulation.?Guan et al. (1990)?invented a process named as the low stress non distortion (LSND) method based on the cross section thermal tensioning effect. LSND was proved to be superior in preventing buckling distortion in butt welding of thin plates.?Guan and Zhang (1994)?developed a dynamic controlling low stress non distortion (DC-LSND) method as another active in-process buckling control method. In this method, a localized thermal tensioning was realized by a spot heat sink trailing with welding torch, and the longitudinal plastic strain at the zone behind the weld pool was dynamically controlled. Jigs are widely used to assist welding process to avoid rotation distortion in the front of welding heat sources.Hajduk et al. (2009)?described the methodological approach about the design of welding fixtures for robotic cells in spot welding of car bodies based on principles of modularity. Regarding control of welding deformation, there are several reports relating to external constraints and loads.?Park et al. (2012)investigated the angular distortion and residual stress under the various pre-tension states by changing the direction and magnitude of pre-tension stress.?Schenk et al. (2009)?studied the clamping effect on buckling distortion and angular distortion for an overlap joint and T-shape fillet joint. They found that residual stresses and welding distortion were strongly affected by clamping condition.?Shateryana et al. (2012)?investigated the constraint effects on welding deformation and residual stress in aluminum alloy lap joints under three types of local U-shape fixture by performing a 3D finite element analysis.?Ziaee et al. (2009)?studied the influence of boundary conditions on buckling modes during welding thin plates. It was found that external constraint can increase the buckling resistance but can not eliminate buckling. Nevertheless, the quantitative study on control of welding deformation by clamping or jig is rare in literatures. Due to the diversity of design parameters and complexity of welded structures, the limited experimental results at some constraint conditions are not enough to provide an overview of the constraint effect. Since the thermal elastic plastic FEM for welding thermal stress was established by?Ueda and Yamakawa (1971), it has been widely used in researches and in solving engineering problems as described by?Ueda et al. (2012). With the great progress of technology in computer aided engineering (CAE), a series of numerical experiments can be efficiently performed without extra cost when the simulation accuracy was verified previously. In this study, prior to investigate the mechanism of the effect of jig constraint on welding deformation, two testing specimens of bead-on-plate welding at a non-constraint free condition and at a jig constraint condition were prepared and welding deformations were measured by a 3D coordinate measuring device. Then the numerical simulation was performed for the two specimens, respectively. The welding deformation predicted by numerical simulation was compared with the experimental results and the simulation validity was accurately verified. Furthermore, to evaluate the effect of jig constraint quantitatively, the jig constraint is classified into two types named as the normal direction constraint and the three-direction constraint. Totally 41 numerical models under various constraint conditions were analyzed. Two parameters?a?and?b, which represent the pitch between two jigs in welding direction and distance from weld line, respectively, were focused and their effect on welding deformation was investigated in details. 2. Experimental study To investigate the effect of constraint by jigs, two specimens were welded at a non-constraint free condition and at a jig constraint condition as shown in?Fig. 1(a) and (b), respectively. In the jig constraint specimen, the jigs were fastened on the platform and out-of-plane deflection was fixed. The dimensions of the specimens are 400?mm in the length, 400?mm in the width and 9?mm in the thickness. The base material of the plate is SS400 and the material of welding wire with a diameter of 1.2?mm is MG-50T. The rust on the plate surface around the weld line was removed before welding for a good welding quality. The room temperature was about 20?°C during experiment. Fig. 1.?Specimens to be welded: (a) at free condition (b) with jig constraint. The single pass bead-on-plate welding was performed by an automatic MAG welding machine using the same welding conditions (240?A, 25?V, 5?mm/s). The shielding gas was 100% CO2. The constraint jigs were removed about 4?min later from the finishing time of welding. The welded specimens are shown in?Fig. 2(a) and (b), respectively. Fig. 2.?Specimens after welding: (a) at free condition (b) with jig constraint. To obtain the welding deformation, small sized holes were drilled on the plate. The center of each hole was recognized as a measuring point. The coordinates at measuring points on the plate were measured before welding and after cooling. By subtracting the initial coordinates from the final ones, welding deformations were calculated. The three typical welding deformation components, longitudinal shrinkage, transverse shrinkage and angular distortion were evaluated using the measured results. The longitudinal shrinkage at the longitudinal sectionsY?=??190, ?40, 40, 190?mm was, respectively, evaluated as shown in?Fig. 3. The transverse shrinkage and angular distortion were evaluated at the transverse sections?X?=?10, 50, 200, 350, 390?mm as shown in?Fig. 4?and?Fig. 5. The deformation values were the averaged ones at the measuring points on the top surface and bottom surface. Fig. 3.?Longitudinal shrinkage under a non-constraint free condition and a jig constraint condition: (a) four longitudinal sections; (b) longitudinal shrinkage. Fig. 4.?Transverse shrinkage under a non-constraint free condition and a jig constraint condition: (a) five transverse sections; (b) transverse shrinkage. Fig. 5.?Angular distortion under a non-constraint free condition and a jig constraint condition: (a) five transverse section lines; (b) angular distortion. Fig. 3?clearly shows that longitudinal shrinkage near the weld line has much larger value than that far away from the weld line.?Fig. 4?and?Fig. 5?show that the transverse shrinkage and angular distortion at the five sections, respectively, are relatively uniform, since the welding heat input per unit weld length is constant. At the finishing end of the weld line, transverse shrinkage decreased because the compressive transverse plastic strain becomes smaller due to the relatively weaker internal constraint at the end. Through the comparison, it was confirmed that if the constraint jigs are employed to clamp the welding specimen, the angular distortion can be greatly reduced compared with that under a non-constraint free condition. The effect of jig constraint on longitudinal shrinkage and transverse shrinkage was relatively smaller comparing with the effect on angular distortion. 3. Numerical simulation In this study, three-dimensional thermal elastic–plastic FEM was employed to simulate the welding thermal stress and deformation. Constraint jigs were modeled in the simulation following the experimental conditions. The interaction between jigs and specimen was considered by fixing the end of jigs. To accurately model the thermal–mechanical behavior during welding, the temperature dependent material properties were employed. The base metal and filler metal were defined separately in the numerical simulation. Temperature and mechanical analysis were performed sequentially, and iterative substructure method (ISM) proposed byMurakawa et al. (2004)?was used in mechanical analysis to save the computation time. 3.1. Finite element model A solid element formulation is generally necessary to analyze the transient welding thermal stress and strain. To fit the temperature gradient around welding heat source, dense mesh should be made in the vicinity of weld line. In this study, hexahedral elements whose robustness and accuracy in dealing with plasticity behavior were proved well by?Benzley (1995), were employed for welding simulations. The finite element model for the constrained welding specimen is shown in?Fig. 6. The shape of the weld reinforcement in the finite element model was determined from experimental observation, and the width and height are 10?mm and 2.2?mm, respectively. The element size in the weld zone is 5?mm in welding direction, 2?mm in the width direction and 1.8?mm in the thickness direction. The numbers of elements and nodes are 15,736, 20,448, respectively. The jigs are also modeled by solid elements to take into account of its elastic constraint. Due to the complexity of jig geometry, each jig is simplified into two cuboids which have the same length and transverse section as the actual jigs, and the clamping face is approximately 15?mm?×?10?mm. Fig. 6.?Finite element mesh for specimen with jigs and welding heat source zone. 3.2. Welding thermal conduction analysis Before mechanical analysis, thermal conduction analysis was performed to obtain the temperature history for all nodes of solid elements. Welding heat source was represented by uniform heat generation rate within a moving volume as shown in?Fig. 6. The temperature dependent physical properties used in the thermal conduction simulation, are shown in?Fig. 7(a). The thermal properties of weld metal (WM) were assumed to be the same with base metal (BM). At the high temperature over 1000?°C, the material properties were considered to be the same with those at 1000?°C. The ambient temperature was set to be 20?°C and the heat transfer coefficient was assumed to be 24?W/(m2?°C) on all the surfaces (Ueda et al., 2012). Fig. 7.?Material properties of base metal and weld metal: (a) thermal physical properties; (b) mechanical properties. In?Fig. 8, the transient temperature field at 40?s was drawn with cross sectional view, from which it can be seen that, the region near heat source has large temperature gradient, while the rear part showed relatively uniform distribution. The maximum reached temperature distribution on the transverse section which indicates the fusion zone is shown in?Fig. 9. Fig. 8.?Transient temperature distribution at 40?s from start of welding: (a) global view; (b) sectional view. Fig. 9.?The maximum reached temperature distribution on transverse section and fusion zone. 3.3. Thermal stress and deformation analysis By applying the transient temperature, welding thermal stress and deformation were computed incrementally for each time step. The mechanical properties of base metal and filler metal are shown in?Fig. 7(b). The properties of the base metal and filler metal are the same except for the yield stress. The materials follow the isotropic hardening law and related plastic flow rule. For the model welded under a non-constraint free condition, only rigid body motion was restricted in finite element model. For the jig constraint specimen, the end of jigs was constrained in the plate normal direction (Z-direction) during welding. The jig constraint was released after welding. The phase transformation behavior (?Deng, 2009) were not considered in the simulation. The iterative substructure method (ISM) was adopted in order to save computation time without loss of accuracy. Basically, the whole model A was divided into two regions with different level of nonlinearity as shown in?Fig. 10. In the present study, the B region was defined by elements in which the temperature is higher than 300?°C. The remaining region excluding the B region from whole model A is defined as A–B region. The A–B region and B region are solved in an interactive manner, and the unbalanced force on the boundary between the two regions is computed iteratively until equilibrium is satisfied. In this way, total number of iteration steps for whole region will be greatly reduced compared with the straightforward scheme. Fig. 10.?Schematic drawing of regions A, B and A–B in the framework of ISM. 4. Comparison of welding deformation The distributions of computed out-of-plane displacement in the?z?direction under the non-constraint free condition and the jig constraint condition are shown in?Fig. 11. It can be easily observed that the out of plane distortion has been greatly reduced by jig constraint. Fig. 11.?Out-of-plane deformation (unit: mm, deformation scale: 10 times): (a) specimen under free condition; (b) specimen with jigs. The comparisons of welding deformation between simulation and measurement at the non-constraint free condition were shown in?Fig. 12(a)–(c). The computed longitudinal shrinkage as shown in?Fig. 12(a) is symmetrical to the weld line due to the symmetry of the model. The longitudinal shrinkage near the edge of plate is much smaller than that close to weld line. Fig. 12.?Welding deformations at a non-constraint free condition and the comparison between experiment and simulation: (a) longitudinal shrinkage; (b) transverse shrinkage; (c) angular distortion. From the computed and measured results, it can be found that the transverse shrinkage at the middle section of plate is larger than that near the edge as shown in?Fig. 12(b). The smallest value appears at the finishing end of welding. The angular distortion changes a little at all five transverse sections as shown in?Fig. 12(c). If it is observed in detail, the angular distortion at the transverse sections near the terminal of the weld line is larger than that near the starting side of weld line. This is because the pre-heating effect from moving welding heat source is strong near the terminal of the weld line and a pre-angular distortion has been produced in the front of welding heat source. The computed longitudinal shrinkage, transverse shrinkage and angular distortion were very close to the experimental ones. For the specimen under the jig constraint conditions, comparison of angular distortion between experiment and simulation was made and shown in?Fig. 13. Both the experimental and simulation results show that there was about 70% reduction in the angular distortion if constraint jigs were employed. Fig. 13.?Measured and computed welding angular distortion with jig constraint. 5. Parametric study of jig constraint 5.1. Models of jig constraint conditions If jigs constrain the plates through contact, the displacement only in the normal direction of the contact faces between plates and jigs can be assumed to be constrained. If the jigs are rigidly fixed with the plates to be welded, the displacement at the jig constraint positions can be assumed to be fully fixed in the three directions. In this study, two types of constraint from jigs, simply named as the normal direction jig constraint and the three-direction jig constraint, are assumed and schematically shown in?Fig. 14. Fig. 14.?Configuration of jigs and two types of jig constraint. In the modeling of the normal direction jig constraint, nodes on the top and bottom surfaces with distance?baway from weld line, representing the jig constraint position, are fixed only in the normal direction. Additional constraint at nodes 20?mm away from weld line is employed to model supporting base on the bottom surface of plate. In the three-direction jig constraint condition, the displacement at the nodes where jigs were set, is fixed in the three directions. In all cases, the jig constraint at the nodes was applied from the beginning of welding and released after 220?s when the welding was finished. The simulations were performed for a bead-on-plate welding model with dimensions 400?mm?×?400?mm?×?10?mm. The jigs were symmetrically arranged on both sides of welding line. For the sake of simplicity, the constraints are directly applied at the nodes on the top and bottom surfaces for each jig. To investigate the effect of jig position and pitch on welding deformation, totally 41 cases of numerical simulations shown in?Table 1?were performed including one case under a non-constraint free condition. Table 1. Numerical simulation conditions and cases with various jig constraints. Constraint types Jig position?b?(mm) Jig pitch?a?(mm) Total cases Non-constraint free condition None None 1 Normal direction jig constraint 30, 50, 100, 200 5, 20, 40, 80, 200 20 Three direction jig constraint 30, 50, 100, 200 5, 20, 40, 80, 200 20 The welding deformation components, tendon force?F, transverse shrinkage and angular distortion on the middle cross section were investigated. The concept of tendon force was originally proposed by?White et al. (1980)?to represent the lo