Failure Analysis of Fracture of High Strength Steel Spot-welded Joints about Cross Tension Testing

高强钢点焊熔合界面正向拉伸撕裂失效评价分析 Failure Analysis of Fracture of High Strength Steel Spot-welded Joints about Cross Tension Testing first-author 金泉军（1977—），男，硕士，高级工程师，主要从事汽车材料开发与轻量化技术的研究。 金泉军（1977—），男，硕士，高级工程师，主要从事汽车材料开发与轻量化技术的研究。 浙江吉利远程新能源商用车集团有限公司，浙江 杭州 311228 浙江吉利远程新能源商用车集团有限公司，浙江 杭州 311228 Zhejiang Geely New Energy Commercial Vehicle Groud Co., Ltd., Hangzhou 311228, China Zhejiang Geely New Energy Commercial Vehicle Groud Co., Ltd., Hangzhou 311228, China 基于界面撕裂和熔核剥离两种模式下焊点的不同应力分布规律，通过应用极限应力理论及Mises应力，计算两种失效模式下高强度钢焊点的最大载荷，推导出界面撕裂失效时的临界熔核直径 <math id="M1"><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><mroot><mrow><mn mathvariant="normal">3</mn></mrow><mrow/></mroot><mo>/</mo><mn mathvariant="normal">3</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn mathvariant="normal">2</mn><mi>n</mi><mo>+</mo><mn mathvariant="normal">2</mn><mo stretchy="false">)</mo><mi>t</mi><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mi>I</mi><mi mathvariant="normal">%</mi><mo stretchy="false">)</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">A</mi><mi mathvariant="normal">Z</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485567&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485565&type= 52.40866470 4.06400013 。通过正交试验方法对高强钢焊点正向失效模式进行分析验证，结果发现，当实测熔核直径小于临界熔核直径时，焊点发生明显的界面撕裂模式；当实测熔核直径大于临界熔核直径时，发生明显的熔核剥离模式；焊接电流对高强度钢的焊点熔核直径影响最大，对焊点失效方式有较大影响。 According to the different stress distribution under interfacial fracture mode and button pull-out mode, the maximum force on high strength steel spot-welded joints for two kinds of failure modes were analysised and calculated based on Mises criteria and ultimate stress theory.The critical weld diameter <math id="M2"><msub><mrow><mi>d</mi></mrow><mrow><mi>c</mi><mi>r</mi><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><mroot><mrow><mn mathvariant="normal">3</mn></mrow><mrow/></mroot><mo>/</mo><mn mathvariant="normal">3</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn mathvariant="normal">2</mn><mi>n</mi><mo>+</mo><mn mathvariant="normal">2</mn><mo stretchy="false">)</mo><mi>t</mi><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mi>I</mi><mi mathvariant="normal">%</mi><mo stretchy="false">)</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">A</mi><mi mathvariant="normal">Z</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485576&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485572&type= 52.49333191 4.06400013 for interfacial tearing failure was calculated.High strength steel was used to validate the critical weld diameter by the orthogonal test.The results showed that when the measured nugget diameter was smaller than the critical nugget diameter, interfacial fracture mode appeared in the welding nugget; when the measured nugget diameter was larger than the critical nugget diameter, button pull-out mode appeared. At the same time, the welding current had the greatest effect on the nugget diameter to resistance spot welding of high strength steel, and it had a great effect on the fracture mode of sold-welded joints. 高强度钢 界面撕裂 熔核剥离 正向拉伸 失效分析 熔核直径 high strength steel interfacial fracture button pull-out cross-tensile failure analysis nugget diameter 前言 1 随着全球能源与环境危机的日益加重，节能减排已成为当代汽车设计和制造所面临的重要课题 ［ 1 1 - 2 2 1-2 ］ 。研究表明，燃油消耗的50%是汽车自重引起的，减少车重成为降低燃油消耗的最有效措施 ［ 3 3 - 4 4 3-4 ］ 。目前各大主机厂广泛应用高强度钢，但由于其含碳量较低及合金元素含量较高等特点，在进行电阻点焊时，熔化的高温奥氏体在快速冷却（约2 000 ℃/s）形成熔核的过程中，其温度变化曲线会直接穿越马氏体相变临界区域，熔核中会产生不同含量和分布的马氏体 ［ 5 5 - 7 7 5-7 ］ ，易产生气孔、裂纹及内部残余应力分布不均等缺陷。因此，当进行焊点拉剪力学性能测试时，焊点失效模式除传统的熔核剥离（Button Pull-out）外，还将出现从熔核区界面撕裂（Interfacial Fracture）的模式 ［ 8 8 - 9 9 8-9 ］ ，传统经验公式 <math id="M3"><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">4</mn><mroot><mrow><mi>t</mi></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485584&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485580&type= 14.05466747 4.57200003 将难以适用，无法保证在力学测试时获得焊点撕裂失效模式。 焊点界面撕裂的力学性能因素表明 ［ 10 10 ］ ，当熔核受拉剪力作用时，焊点的不同失效模式是由对应失效区所能承受的极限应力决定：发生焊点界面撕裂模式是由于熔核界面的拉应力 <math id="M4"><mi>σ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485590&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485588&type= 1.94733346 2.62466669 达到极限值 <math id="M5"><msub><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485597&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485594&type= 5.41866684 3.72533321 ；发生焊点熔核剥离模式是由于熔核周边热影响区受到的剪应力 <math id="M6"><mi>τ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485605&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485602&type= 1.43933344 2.62466669 达到极限值 <math id="M7"><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485714&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485713&type= 4.91066647 3.72533321 。而影响焊点力学性能的因素主要是焊点的熔核直径、压痕等形貌，因此，迫切需要建立新的熔核直径理论评价模型来评价焊点界面撕裂问题。 本文针对焊点力学测试中采用的正向拉伸试验方式，对高强度钢点焊焊点进行力学建模分析，根据两种不同失效模式（界面撕裂和熔核剥离）下焊点所能承受最大载荷来计算临界熔核直径，进而获得评价焊点失效模式的特征指标，并通过正交试验方法对理论推导结果进行验证。 焊点界面撕裂评价模型建立 1 不同失效模式时焊点受载分析 2 界面撕裂模式下的焊点受载 3 将焊点假设为圆柱体，如 图1 图1 所示。在进行拉伸试验时，熔核区承受切向剪切应力，假设熔核直径为 <math id="M8"><mi>d</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485977&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485971&type= 2.20133328 2.70933342 （半径为 <math id="M9"><mi>r</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485626&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485623&type= 1.52400005 2.62466669 ），熔核区厚度为 <math id="M10"><mn mathvariant="normal">2</mn><mi>t</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485691&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485689&type= 2.96333337 2.62466669 ，所受的拉伸力为 <math id="M11"><msub><mrow><mi>F</mi></mrow><mrow><mi mathvariant="normal">t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485637&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485634&type= 8.21266651 3.72533321 。在发生焊点界面撕裂模式时，由于熔核界面剪应力 τ 达到最大承受极限 <math id="M12"><msubsup><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485644&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485641&type= 7.19666624 4.06400013 。此时假设熔核内部组织均匀，纯拉剪状态焊点界面剪应力分布为均匀分布，如 图2 图2 所示，图中“×”表示应力分布点。 图中“×”的微分面积为： <math display="block" id="M13"><mi mathvariant="normal">d</mi><mi>s</mi><mo>=</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><mi>x</mi><mi mathvariant="normal">d</mi><mi>x</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485665&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485663&type= 15.49400043 2.62466669 式中　 x 为从焊核中心到某处的距离。 则剪应力 <math id="M14"><mi>τ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485668&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485667&type= 1.43933344 2.62466669 是“×”的多项式函数： <math display="block" id="M15"><mi>τ</mi><mo>=</mo><mfrac><mrow><msup><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></mfrac><msubsup><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485674&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485672&type= 17.69533348 7.78933382 式中　 R 为界面失效熔核半径； <math id="M16"><msubsup><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485680&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485677&type= 7.70466709 4.06400013 为发生界面撕裂时，熔核界面所能承受的极限拉应力。 熔核界面撕裂时，所能承受的拉伸力为 <math display="block" id="M17"><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>F</mi></mrow><mrow><mi mathvariant="normal">t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>=</mo><mo>∫</mo><mfrac><mrow><msup><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></mfrac><msubsup><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi></mrow></msubsup><mi mathvariant="normal">d</mi><mi>s</mi><mo>=</mo><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><mi>R</mi></mrow></msubsup><mrow><mfrac><mrow><msup><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></mfrac><msubsup><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi></mrow></msubsup><mo>×</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><mi>x</mi></mrow><mi mathvariant="normal">d</mi><mi>x</mi></mtd></mtr><mtr><mtd><mtext>            </mtext><mo>=</mo><mfrac><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></mfrac><msubsup><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi></mrow></msubsup><mi mathvariant="normal">π</mi><msup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485685&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485683&type= 64.00800323 16.84866714 式中　其中 <math id="M18"><msub><mrow><mi>F</mi></mrow><mrow><mi mathvariant="normal">t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485688&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485686&type= 8.21266651 3.72533321 为发生界面撕裂（Interfacial Fracture）模式时，熔核所能承受的最大拉伸力。 熔核剥离模式下的焊点受载 3 熔核剥离模式下，整个熔核从母材中分离，失效位置为熔核周边热影响区，由于该区域承受的剪应力达到所能承受的极限应力，而最终导致失效。 此时焊点的受力模型如 图3 图3 所示，假设熔核厚度为 <math id="M19"><mn mathvariant="normal">2</mn><mi>t</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485691&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485689&type= 2.96333337 2.62466669 ，熔核失效处直径为 <math id="M20"><mi>d</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485977&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485971&type= 2.20133328 2.70933342 ，在拉剪力作用下，熔核失效区的边缘圆周受到均匀的极限拉剪应力（见 图4 图4 ）。 则位置 <math id="M21"><mi>θ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485708&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485706&type= 1.86266661 2.62466669 处的微分面积为： <math display="block" id="M22"><mi mathvariant="normal">d</mi><mi>s</mi><mo>=</mo><mi>r</mi><mo>⋅</mo><mi>t</mi><mo>⋅</mo><mi mathvariant="normal">d</mi><mi>θ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485711&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485709&type= 17.18733406 2.62466669 式中　 t 为铝合金厚度； r 为剥离失效熔核半径。 由于该位置的剪应力为 <math id="M23"><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485714&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485713&type= 4.91066647 3.72533321 ，故该处的剪力微分为： <math display="block" id="M24"><mi mathvariant="normal">d</mi><msub><mrow><mi>F</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">O</mi></mrow></msub><mo>=</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub><mo>⋅</mo><mi>r</mi><mo>⋅</mo><mi>t</mi><mo>⋅</mo><mi mathvariant="normal">d</mi><mi>θ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485718&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485716&type= 27.68600082 3.72533321 熔核剥离时，所能承受的最大剪力为 <math display="block" id="M25"><msub><mrow><mi>F</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">O</mi></mrow></msub><mo>=</mo><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi></mrow></msubsup><mrow><mi>r</mi><mo>⋅</mo><mi>t</mi><mo>⋅</mo><msubsup><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">A</mi><mi mathvariant="normal">Z</mi></mrow></msubsup></mrow><mo>⋅</mo><mi mathvariant="normal">d</mi><mi>θ</mi><mo>=</mo><mi mathvariant="normal">π</mi><mi mathvariant="normal">d</mi><mi>t</mi><msubsup><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">A</mi><mi mathvariant="normal">Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485723&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485720&type= 46.65133286 7.53533268 式中　 <math id="M26"><msub><mrow><mi>F</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">O</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485726&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485724&type= 5.07999992 3.72533321 为发生熔核剥离模式时，熔核所能承受的最大剪力； <math id="M27"><msubsup><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">A</mi><mi mathvariant="normal">Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485729&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485727&type= 5.84200001 4.06400013 为发生熔核剥离时，熔核失效界面所能承受的极限剪应力。 临界失效模式熔核直径计算模型 2 综上所述，当焊点发生临界失效模式时，根据 式（3） 式（3） 与 式（6） 式（6） ，熔核所能承受的拉力 <math id="M28"><msub><mrow><mi>F</mi></mrow><mrow><mi mathvariant="normal">t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485733&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485731&type= 8.21266651 3.72533321 与 <math id="M29"><msub><mrow><mi>F</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">O</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485740&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485737&type= 5.07999992 3.72533321 应相等。 此时： <math display="block" id="M30"><mtable columnalign="left"><mtr><mtd><mfrac><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></mfrac><msubsup><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi></mrow></msubsup><mi mathvariant="normal">π</mi><msup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>=</mo><mi mathvariant="normal">π</mi><mi mathvariant="normal">d</mi><mi>t</mi><msubsup><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">A</mi><mi mathvariant="normal">Z</mi></mrow></msubsup></mtd></mtr><mtr><mtd><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn><mi>n</mi><mo>+</mo><mn mathvariant="normal">2</mn></mrow></mfrac><msubsup><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi></mrow></msubsup><mi mathvariant="normal">π</mi><msup><mrow><mi>d</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>=</mo><mi mathvariant="normal">π</mi><mi mathvariant="normal">d</mi><mi>t</mi><msubsup><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">A</mi><mi mathvariant="normal">Z</mi></mrow></msubsup></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485745&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485742&type= 37.25333405 16.34066582 因发生界面撕裂时，失效在熔核区；而发生熔核剥离时，失效在热影响区。故 式（7） 式（7） 可转化为： <math display="block" id="M31"><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><mn mathvariant="normal">2</mn><mi>n</mi><mo>+</mo><mn mathvariant="normal">2</mn><mo stretchy="false">)</mo><mi>t</mi><msubsup><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">A</mi><mi mathvariant="normal">Z</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi></mrow></msubsup><mi mathvariant="normal">　</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485750&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485748&type= 37.50733566 4.91066647 （ n ≥1） 式中　 <math id="M32"><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485756&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485753&type= 3.55599999 3.80999994 为临界熔核直径。 根据von Mises应力失效准则，材料所能承受的极限拉应力为极限剪应力的 <math id="M33"><mroot><mrow><mn mathvariant="normal">3</mn></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485765&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485760&type= 5.58799982 4.31799984 倍，故 式（8） 式（8） 可转化为： <math display="block" id="M34"><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi></mrow></msub><mo>=</mo><mfrac><mrow><mroot><mrow><mn mathvariant="normal">3</mn></mrow><mrow/></mroot></mrow><mrow><mn mathvariant="normal">3</mn></mrow></mfrac><mo stretchy="false">(</mo><mn mathvariant="normal">2</mn><mi>n</mi><mo>+</mo><mn mathvariant="normal">2</mn><mo stretchy="false">)</mo><mi>t</mi><msubsup><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">A</mi><mi mathvariant="normal">Z</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485772&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485767&type= 40.89400101 8.21266651 由于在焊接压力作用下，焊接熔核区域会出现一定的压痕深度，因此考虑压痕影响。可得： <math display="block" id="M35"><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mi>I</mi><mi mathvariant="normal">%</mi><mo stretchy="false">)</mo><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485778&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485776&type= 22.43666649 4.48733330 式中 　I %为压痕深度。根据HB5276—84、HB5282—84标准规定： I %≤20%。 根据材料的极限拉应力与维氏硬度的比例关系 ［ 11 11 - 12 12 11-12 ］ 为 <math display="block" id="M36"><msub><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">U</mi><mi mathvariant="normal">T</mi><mi mathvariant="normal">S</mi></mrow></msub><mo>=</mo><mi>C</mi><mo>×</mo><mi>H</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485786&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485782&type= 17.78000069 3.72533321 式中　 C 为常数； H 为材料的维氏硬度。 则 式（9） 式（9） 改为： <math display="block" id="M37"><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mroot><mrow><mn mathvariant="normal">3</mn></mrow><mrow/></mroot></mrow><mrow><mn mathvariant="normal">3</mn></mrow></mfrac><mo stretchy="false">(</mo><mn mathvariant="normal">2</mn><mi>n</mi><mo>+</mo><mn mathvariant="normal">2</mn><mo stretchy="false">)</mo><mi>t</mi><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mi>I</mi><mi mathvariant="normal">%</mi><mo stretchy="false">)</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">A</mi><mi mathvariant="normal">Z</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485792&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485788&type= 56.55733109 8.21266651 式中　 <math id="M38"><msubsup><mrow><mi>H</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">A</mi><mi mathvariant="normal">Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485800&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485795&type= 7.53533268 4.06400013 为母材的维氏硬度； <math id="M39"><msubsup><mrow><mi>H</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485805&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485802&type= 8.80533314 4.06400013 为焊核的维氏硬度。 试验材料和方法 1 试验材料 2 试验采用马钢生产的2.0 mm厚DP800钢板材料，其化学成分如 表1 表1 所示。从组织检验结果可以看出，该钢种显微组织主要为马氏体和铁素体，通过SEM扫面电镜可以看出在铁素体晶界内存在弥散分布的细小颗粒，可能是碳化物或者是马奥岛组织 ［ 13 13 - 14 14 13-14 ］ ，材料的力学性能如 图5 图5 所示。 C Mn Cr Si Mo Nb Ni P+S 0.07 2.21 0.016 1.05 0.03 0.022 0.017 少量 试验方法 2 根据文献［ 15 15 ］将试验钢板采用方盒冲压形件，尺寸如 图6a 图6a 所示。将冲压后的拉伸试样（见 图6b） 图6b） 在Bosch6000中频点焊机设备上进行焊接，其中额定工作电极压力7 kN，额定焊接电流23 kA，输出功率130 kW。由于点焊过程中的电流、时间（包括焊接时间和保持时间）、焊接压力是影响焊点质量的重要因素，因此，分析焊接时间、焊接电流、焊接压力、保持时间四个因素对焊点界面撕裂程度的影响。使用L 9 （4 4 ）的正交试验设计表，因素水平设置如 表2 表2 所示，为4因素4水平。焊接后的试样在WE230拉伸试验机上以2 mm/min的速度进行拉伸试验，以检测焊后熔核失效模式。然后对其进行切割、镶嵌、打磨、抛光、腐蚀等工序，在显微镜下观察熔核，并测量熔核直径 <math id="M40"><mi>d</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485977&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485971&type= 2.20133328 2.70933342 。采用硬度仪HV-1000测量熔核区与热影响区的维氏硬度。焊点拉伸后有两种失效模式：界面撕裂模式和熔核剥离模式（见 图7 图7 ）。以熔核直径作为衡量焊点撕裂程度的指标，在焊点无缺陷情况下，实际熔核直径与临界熔核直径比值作为评判焊点强度的指标，比值大于1为焊点熔核剥离失效，焊点抗拉强度满足要求；反之比值小于1为焊点界面撕裂失效，焊点抗拉强度不满足要求。 水平 焊接电流/A 焊接压力/N 焊接时间/周波 保温时间/周波 1 6 500 2 000 10 10 2 7 500 2 500 12 12 3 8 500 3 000 15 15 4 9 500 3 500 18 18 1,2; 1;2; 试验结果及分析 1 试验设计结果 2 试验共16组，每一组试验分别进行4次焊接，并对焊后试片进行正向拉伸检测，测量焊后熔核直径，取平均值进行统计。然后计算各因素在各水平下的平均值与极差以及方差分析结果，结果如 表3 表3 ~ 表5 表5 所示。 试验 焊接电流/A 焊接时间/CYC 焊接压力/N 保温时间/周波 H HAZ / H nugget 压痕/％ 熔核直径/mm 失效模式 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 6 500 6 500 6 500 6 500 7 500 7 500 7 500 7 500 8 500 8 500 8 500 8 500 9 500 9 500 9 500 9 500 10 12 15 18 10 12 15 18 10 12 15 18 10 12 15 18 2 000 2 500 3 000 3 500 2 500 2 000 3 500 3 000 3 000 3 500 2 000 2 500 3 500 3 000 2 500 2 000 10 12 15 18 15 18 10 12 18 15 12 10 12 10 18 15 284/380 288/370 287/372 284/370 288/367 284/372 288/372 289/370 288/367 288/368 288/374 285/372 288/372 289/370 282/368 288/372 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 3.0 3.3 3.37 3.71 4.12 4.36 4.61 4.85 5.0 5.34 5.49 5.67 6.0 6.4 6.37 6.73 界面 界面 界面 界面 界面 界面 界面 界面 界面 剥离 剥离 剥离 剥离 剥离 剥离 剥离 试验 临界直径值 <math id="M41"><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi><mn>1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485906&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485902&type= 3.55599999 2.70933342 （ n =1） 临界直径值 <math id="M42"><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi><mn>2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485913&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485909&type= 3.55599999 2.70933342 （ n =2） 临界直径值 <math id="M43"><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi><mn>3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485921&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485916&type= 3.55599999 2.70933342 （ n =3） 临界直径值 <math id="M44"><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi><mn>4</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485931&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485926&type= 3.55599999 2.70933342 （ n =4） 比值（ <math id="M45"><mi>μ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485956&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485952&type= 1.52400005 2.45533323 1 ） 比值（ <math id="M46"><mi>μ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485956&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485952&type= 1.52400005 2.45533323 2 ） 比值（ <math id="M47"><mi>μ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485956&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485952&type= 1.52400005 2.45533323 3 ） 比值（ <math id="M48"><mi>μ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485956&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485952&type= 1.52400005 2.45533323 4 ） 1 2.759 882 4.139 823 5.519 764 6.899 705 1.087 003 0.724 669 0.543 501 0.434 801 2 2.674 785 4.012 177 5.349 57 6.686 962 1.233 744 0.822 496 0.616 872 0.493 498 3 2.650 477 3.975 716 5.300 955 6.626 194 1.271 469 0.847 646 0.635 735 0.508 588 4 2.634 863 3.952 294 5.269 725 6.587 157 1.408 043 0.938 695 0.704 022 0.563 217 5 2.696 65 4.044 974 5.393 299 6.741 624 1.527 822 1.018 548 0.763 911 0.611 129 6 2.719 966 4.079 948 5.439 931 6.799 914 1.602 961 1.068 641 0.801 481 0.641 185 7 2.660 404 3.990 606 5.320 809 6.651 011 1.732 819 1.155 213 0.866 41 0.693 128 8 2.684 765 4.027 148 5.369 531 6.711 914 1.806 489 1.204 326 0.903 245 0.722 596 9 2.683 892 4.025 838 5.367 784 6.709 729 1.862 966 1.241 978 0.931 483 0.745 187 10 2.715 869 4.073 803 5.431 738 6.789 672 1.966 222 1.310 814 0.983 111 0.786 489 11 2.662 703 3.994 055 5.325 406 6.656 758 2.061 815 1.374 543 1.030 907 0.824 726 12 2.729 892 4.094 839 5.459 785 6.824 731 2.077 005 1.384 67 1.038 502 0.830 802 13 2.687 43 4.031 146 5.374 861 6.718 576 2.232 616 1.488 411 1.116 308 0.893 046 14 2.684 765 4.027 148 5.369 531 6.711 914 2.383 821 1.589 214 1.191 91 0.953 528 15 2.729 461 4.094 191 5.458 922 6.823 652 2.333 794 1.555 863 1.166 897 0.933 518 16 2.660 404 3.990 606 5.320 809 6.651 011 2.529 691 1.686 46 1.264 845 1.011 876 平均1 0.625 032 5 0.900 791 0.910 183 5 0.910 080 7 平均2 0.833 761 8 0.896 545 5 0.896 545 5 0.916 833 平均3 0.996 000 8 0.924 987 3 0.915 593 3 0.911 900 5 平均4 1.184 99 0.977 653 5 0.917 462 8 0.900 970 8 极差 0.559 957 5 0.081 108 0.020 917 2 0.009 11 注： ★0.05水平显著，★★0.01水平显著，★★★ < 0.000 1水平显著。 方差来源 自由度 偏差平方和 F 比值 P 值 显著性 焊接电流 焊接时间 焊接压力 保温时间 误差 总和 3 3 3 3 3 15 0.680 137 5 0.020 295 6 0.001 072 1 0.000 527 3 0.021 810 6 0.723 843 1 31.183 743 0.930 537 0.049 154 5 0.027 176 1 0.009 2 0.523 0.983 0.994 ★★ 由于在试验中主要以实际的熔核直径与理论熔核直径比值作为评判焊点质量的指标。根据失效模式，明显发现其临界熔核直径值为 式（12） 式（12） 中 n =3时与试验的失效模式过程较为吻合。通过极差分析可知，影响熔核直径的关键因素依次为焊接电流、焊接时间、焊接压力和保温时间。使用方差显著性分析，焊接电流的 P =0.009 2，小于0.01，其他因素的 P 值均大于0.05，由此可知对焊点撕裂失效的关键因素为焊接电流，其他因素对焊点失效影响较小。较小的电流容易产生界面失效，主要原因是焊接热量不足，无法形成足够大的熔核直径导致界面失效；然而随着焊接电流的增加，熔合直径增大到一定程度后会产生剥离失效。焊接时间、焊接压力、保温时间等工艺参数对焊点撕裂失效程度影响不明显。 焊点熔核直径结果分析 2 将测得熔核直径 <math id="M49"><mi>d</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485977&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485971&type= 2.20133328 2.70933342 、正向拉伸强度进行统计，并参考 式（3） 式（3） 、 式（6） 式（6） 、 式（12） 式（12） 计算出 <math id="M50"><msub><mrow><mi>F</mi></mrow><mrow><mi mathvariant="normal">t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485987&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485982&type= 8.21266651 3.72533321 、 <math id="M51"><msub><mrow><mi>F</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">O</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485994&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485989&type= 5.07999992 3.72533321 、 <math id="M52"><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486001&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39485998&type= 3.55599999 3.80999994 及直径比 <math id="M53"><mi>μ</mi><mo>=</mo><mi>d</mi><mo>/</mo><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486008&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486005&type= 12.78466606 4.48733330 ，结果如 表6 表6 所示。 注： <math id="M58"><mi>μ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486042&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486041&type= 1.52400005 2.45533323 大于1为剥离失效， <math id="M59"><mi>μ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486042&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486041&type= 1.52400005 2.45533323 小于1为界面失效。 试验 实际直径/mm H HAZ /H nugget 实际正向拉伸强度/N <math id="M54"><msub><mrow><mi>F</mi></mrow><mrow><mi mathvariant="normal">t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>/</mo><mi mathvariant="normal">N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486013&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486010&type= 9.48266602 2.70933342 （ n =3）界面失效 <math id="M55"><msub><mrow><mi>F</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">O</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486020&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486016&type= 3.89466691 2.70933342 /N剥离失效 <math id="M56"><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi><mn>1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486026&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486023&type= 3.55599999 2.70933342 /mm <math id="M57"><mi>μ</mi><mo>=</mo><mi>d</mi><mo>/</mo><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi><mn>1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486032&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486029&type= 9.39799976 3.21733332 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 3.0 3.3 3.37 3.71 4.12 4.36 4.61 4.85 5.0 5.34 5.49 5.67 6.0 6.4 6.37 6.73 284/380 288/370 287/372 284/370 288/367 284/372 288/372 289/370 288/367 288/368 288/374 285/372 288/372 289/370 282/368 288/372 4 678.8 5 276.8 5 845.3 7 045.2 8 243.2 9 287.6 10 245.3 11 213.4 12 023.1 12 945.6 14 987.5 15 789.4 16 213.5 17 245.8 17 025.3 18 435.2 4 192.48 4 870.801 5 124.885 6 411.747 7 530.63 8 668.837 9 556.868 10 484.57 11 091.16 12 685.31 — — — — — — — — — — — — — — — 13 730.63 14 116.32 14 116.32 15 427.67 16 456.18 16 379.04 17 304.7 5.52 5.35 5.3 5.27 5.39 5.44 5.32 5.37 5.37 5.43 5.33 5.46 5.37 5.37 5.46 5.32 0.543 501 0.616 872 0.635 735 0.704 022 0.763 911 0.801 481 0.866 41 0.903 245 0.931 483 0.983 111 1.030 907 1.038 502 1.116 308 1.191 91 1.166 897 1.264 845 分析测试结果发现，当实测熔核直径小于临界熔核直径（ <math id="M60"><mi>μ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486069&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486067&type= 2.11666679 3.38666677 < 1）时，如1~9组试样，焊点发生明显的界面撕裂模式；当实测熔核直径大于临界熔核直径（ <math id="M61"><mi>μ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486069&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486067&type= 2.11666679 3.38666677 > 1）时，如11~16组试样，发生明显的熔核剥离模式；当实测熔核直径与临界熔核直径相近（ <math id="M62"><mi>μ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486069&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486067&type= 2.11666679 3.38666677 ≈1）时，如10组试样，发生临界失效模式（从界面撕裂转为熔合剥离），公式判断结果与试验相符。由此可见，采用 式（12） 式（12） 计算的临界熔核直径能够准确地评价焊点的不同失效模式。 若采用传统的熔核直径经验公式 <math id="M63"><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">4</mn><mroot><mrow><mi>t</mi></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486060&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486058&type= 14.05466747 4.57200003 （厚度为2.0 mm），合格熔核直径≥5.66 mm，按照经验公式要求，10~11组试样试验的熔核直径均不满足设计要求，可判定为界面撕裂模式，但实际却出现明显剥离撕裂模式，故经验公式并不适用。 若不考虑焊点压痕的影响，按照式（1）~ 式（9） 式（9） 进行计算发现：11~15组试样的临界熔核直径均大于实测熔核直径，基于失效评价模式，11~15组试样焊点失效均为界面撕裂模式，但明显与实际不符。因此，计算失效模式下的焊点临界熔核直径时，必须考虑压痕的作用。同时若不考虑实际的焊核与母材的硬度值，会直接影响熔核直径的结果。 结论 1 焊点失效的理论推导公式可以给生产工艺提供正确的评判依据，同时也可以作为整车在受力状况下焊点失效一种评价方式。 （1）通过研究受力模型推导的熔核直径发现，该临界熔核直径评价模型能够有效评价焊点的失效模式，采用 <math id="M64"><mi>μ</mi><mo>=</mo><mi>d</mi><mo>/</mo><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486063&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486062&type= 12.78466606 4.48733330 可以对焊点失效模式进行评价， <math id="M65"><mi>μ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486069&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486067&type= 2.11666679 3.38666677 < 1焊点发生明显的界面撕裂模式， <math id="M66"><mi>μ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486069&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486067&type= 2.11666679 3.38666677 > 1发生明显的熔核剥离模式。 （2）该临界熔核直径与母材维氏硬度、焊核维氏硬度以及压痕深度有一定关系。与传统经验公式对比，采用 <math id="M67"><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><mroot><mrow><mn mathvariant="normal">3</mn></mrow><mrow/></mroot><mo>/</mo><mn mathvariant="normal">3</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn mathvariant="normal">2</mn><mi>n</mi><mo>+</mo><mn mathvariant="normal">2</mn><mo stretchy="false">)</mo><mi>t</mi><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mi>I</mi><mi mathvariant="normal">%</mi><mo stretchy="false">)</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">A</mi><mi mathvariant="normal">Z</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486073&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=39486071&type= 60.02866364 4.65666676 理论公式可以明显提高焊点质量评价准确性。 （3）使用正交试验设计分析可知，焊接电流对高强度钢点焊的熔核直径影响最大，并对焊点撕裂程度也有较大的影响。 参考文献 李永兵 ， 李亚庭 ， 楼铭 ， 等 . 轿车车身轻量化及其对连接技术的挑战 ［J］. 机械工程学报 ， 2012 ， 48 （ 18 ）： 44 - 54 . 轿车车身轻量化及其对连接技术的挑战 LI Y B ， LI Y T ， LOU M ， et al . Lightweighting of Car Body and Its Challenges to Joining Technologies ［J］. Journal of Mechanical Engineering ， 2012 ， 48 （ 18 ）： 44 - 54 . Lightweighting of Car Body and Its Challenges to Joining Technologies 李永兵 ， 马运五 ， 楼铭 ， 等 . 轻量化多材料汽车车身连接技术进展 ［J］. 机械工程学报 ， 2016 ， 52 （ 24 ）： 1 - 23 . 轻量化多材料汽车车身连接技术进展 LI Y B ， MA Y W ， LOU M ， et al . Advances in Welding and Joining Processes of Multi-material Lightweight Car Body ［J］. Journal of Mechanical Engineering ， 2016 ， 52 （ 24 ）： 1 - 23 . Advances in Welding and Joining Processes of Multi-material Lightweight Car Body 马鸣图 . 汽车结构用钢的进展 ［J］. 汽车工程 ， 2005 ， 27 （ 3 ）： 269 - 273 . 汽车结构用钢的进展 MA M T . The Recent Progress of Automotive Structure Steel Products ［J］. Automotive Engineering ， 2005 ， 27 （ 3 ）： 269 - 273 . The Recent Progress of Automotive Structure Steel Products 马鸣图 ， 易红亮 ， 路洪洲 ， 等 . 论汽车轻量化 ［J］. 机械工程材料 ， 2009 ， 11 （ 9 ）： 20 - 27 . 论汽车轻量化 MA M T ， YI H L ， LU H Z ， et al . On the lightweighting of automobile ［J］. 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