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Article(id=1246045610130916218, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246045605047415288, articleNumber=null, orderNo=null, doi=10.19636/j.cnki.cjsm42-1250/o3.2024.020, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1716480000000, receivedDateStr=2024-05-24, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1775010023862, onlineDateStr=2026-04-01, pubDate=1729785600000, pubDateStr=2024-10-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1775010023862, onlineIssueDateStr=2026-04-01, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1775010023862, creator=13701087609, updateTime=1775010023862, updator=13701087609, issue=Issue{id=1246045605047415288, tenantId=1146029695717560320, journalId=1241755870837649424, year='2024', volume='45', issue='5', pageStart='565', pageEnd='708', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1775010022651, creator=13701087609, updateTime=1775010094858, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1246045907972636933, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246045605047415288, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1246045907972636934, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246045605047415288, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=638, endPage=651, ext={EN=ArticleExt(id=1246045610432906114, articleId=1246045610130916218, tenantId=1146029695717560320, journalId=1241755870837649424, language=EN, title=Investigation on the Influence of Surface Topography Reconstruction and Yield Strength of High-strength Aluminum Alloys in Additive Manufacturing, columnId=1244229834482757770, journalTitle=Chinese Journal of Solid Mechanics, columnName=Research Paper, runingTitle=null, highlight=null, articleAbstract=

To investigate the impact of surface topography on the mechanical properties of additive manufacturing materials, in this paper, high-strength aluminum alloy specimens were fabricated by the selective laser melting method. The influences of scanning speed, heat treatment, deposition direction, and surface roughness on tensile mechanical properties were examined. The surface topography measured by an optical microscope was reconstructed based on the Fourier series and MATLAB software, and the analytical solution of the stress concentration coefficient of the surface topography was derived using the Airy stress function. Finite element analysis was conducted using ABAQUS software to validate the analytical results. The probability density function of the stress concentration coefficient was obtained through normal fitting, and a method for evaluating the reliability of the material based on yield strength was proposed. The proposed methodology in this paper is of reference significance for the quantification of surface roughness and its effect on yield strength of other additive manufacturing materials and specimens.

, correspAuthors=Pin Wen, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Ziliang Dong, Zhengkun Cheng, Xiaonan Zhang, Pin Wen), CN=ArticleExt(id=1246045616179102709, articleId=1246045610130916218, tenantId=1146029695717560320, journalId=1241755870837649424, language=CN, title=增材制造高强铝合金表面形貌重构及其屈服强度影响规律探究, columnId=1241831201896469478, journalTitle=固体力学学报, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=

为了研究表面形貌对增材制造材料力学性能的影响，本文通过选择性激光熔化方法制备了高强度铝合金试样，研究了扫描速度、热处理、沉积方向、表面粗糙度等对拉伸力学性能的影响，并基于傅里叶级数和MATLABA软件对光学显微镜测量的表面形貌进行了重构，使用Airy应力函数推导获得了表面形貌应力集中系数的解析解. 采用ABAQUS软件进行了有限元分析，对解析结果进行了验证. 通过正态拟合得到应力集中系数的概率密度函数，提出了一种基于屈服强度评估材料可靠性的方法. 本文所提出方法流程为增材制造其他材料及试样表面粗糙度定量化及其对屈服强度影响具有参考意义.

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** E-mail：.
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ArticleFig(id=1246045625175883943, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246045610130916218, language=CN, label=图14, caption=600 mm/s材料表面应力集中系数数据正态拟合图像, figureFileSmall=WmvUwZadAh3oZO6uYzhetA==, figureFileBig=z7NkVRwZLzzpB4q4if3XBw==, tableContent=null), ArticleFig(id=1246045625284935848, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246045610130916218, language=EN, label=Table 1, caption=

Additive manufacturing material processes

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扫描速率（mm*s-1）激光功率（W）热处理
5001500否
60015003否
7001500否
7001500是
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增材制造材料工艺

, figureFileSmall=null, figureFileBig=null, tableContent=
扫描速率（mm*s-1）激光功率（W）热处理
5001500否
60015003否
7001500否
7001500是
), ArticleFig(id=1246045625565954221, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246045610130916218, language=EN, label=Table 2, caption=

Comparison of tensile results in different directions of specimens

, figureFileSmall=null, figureFileBig=null, tableContent=
试样切割方向等效杨氏模量（MPa）平均杨氏模量（MPa）
堆叠方向13594131721333313366
扫描方向13473128771350913286
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试样不同方向拉伸结果对比

, figureFileSmall=null, figureFileBig=null, tableContent=
试样切割方向等效杨氏模量（MPa）平均杨氏模量（MPa）
堆叠方向13594131721333313366
扫描方向13473128771350913286
), ArticleFig(id=1246045625767280817, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246045610130916218, language=EN, label=Table 3, caption=

Tensile test results comparison

, figureFileSmall=null, figureFileBig=null, tableContent=
材料工艺光滑试样粗糙试样
抗拉强度（MPa）断后延伸率（%）屈服强度（MPa）抗拉强度（MPa）断后延伸率（%）屈服强度（MPa）
500 mm/s267.2216.5128.62239.2114.0120.64
600 mm/s283.3117.5149.64265.8516.0139.60
700 mm/s300.8322.0152.43282.6720.0141.63
700 mm/s（h）337.6717.0195.68321.3214.0180.67
), ArticleFig(id=1246045625842778290, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246045610130916218, language=CN, label=表3, caption=

拉伸试验结果对比

, figureFileSmall=null, figureFileBig=null, tableContent=
材料工艺光滑试样粗糙试样
抗拉强度（MPa）断后延伸率（%）屈服强度（MPa）抗拉强度（MPa）断后延伸率（%）屈服强度（MPa）
500 mm/s267.2216.5128.62239.2114.0120.64
600 mm/s283.3117.5149.64265.8516.0139.60
700 mm/s300.8322.0152.43282.6720.0141.63
700 mm/s（h）337.6717.0195.68321.3214.0180.67
), ArticleFig(id=1246045625926664372, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246045610130916218, language=EN, label=Table 4, caption=

Statistical data of stress concentration factor generated by surface morphology

, figureFileSmall=null, figureFileBig=null, tableContent=
扫描速率（mm*s-1）最值均值μ标准差σ粗糙试样屈服强度（MPa）
5002.98/-0.981.000.35120.64
6002.38/-0.151.000.28139.60
7002.34/0.011.000.31141.63
700（h）2.98/-0.781.000.37180.67
), ArticleFig(id=1246045627495334071, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246045610130916218, language=CN, label=表4, caption=

表面形貌产生的应力集中系数统计数据

, figureFileSmall=null, figureFileBig=null, tableContent=
扫描速率（mm*s-1）最值均值μ标准差σ粗糙试样屈服强度（MPa）
5002.98/-0.981.000.35120.64
6002.38/-0.151.000.28139.60
7002.34/0.011.000.31141.63
700（h）2.98/-0.781.000.37180.67
), ArticleFig(id=1246045627579220152, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246045610130916218, language=EN, label=Table 5, caption=

Converted results of the linear regression equation for yield strength

, figureFileSmall=null, figureFileBig=null, tableContent=
扫描速率（mm*s-1）光滑试样屈服强度（MPa）均值μ标准差σ折算结果（MPa）
500128.621.000.35119.22
600149.641.000.28140.76
700152.431.000.31142.48
700（h）195.681.000.37180.62
), ArticleFig(id=1246045627675689146, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246045610130916218, language=CN, label=表5, caption=

屈服强度线性回归方程折算结果

, figureFileSmall=null, figureFileBig=null, tableContent=
扫描速率（mm*s-1）光滑试样屈服强度（MPa）均值μ标准差σ折算结果（MPa）
500128.621.000.35119.22
600149.641.000.28140.76
700152.431.000.31142.48
700（h）195.681.000.37180.62
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增材制造高强铝合金表面形貌重构及其屈服强度影响规律探究
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董子良 1 , 程正坤 2 , 张晓楠 1 , 文聘 1, **
固体力学学报 | 研究论文 2024,45(5): 638-651
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固体力学学报 | 研究论文 2024, 45(5): 638-651
增材制造高强铝合金表面形貌重构及其屈服强度影响规律探究
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董子良1, 程正坤2, 张晓楠1, 文聘1, **
作者信息
  • 1武汉理工大学理学院工程结构与力学系，武汉，430070
  • 2深圳职业技术大学本科教育学院，深圳，518885

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** E-mail：.
Investigation on the Influence of Surface Topography Reconstruction and Yield Strength of High-strength Aluminum Alloys in Additive Manufacturing
Ziliang Dong1, Zhengkun Cheng2, Xiaonan Zhang1, Pin Wen1, **
Affiliations
  • 1Department of Engineering Structures and Mechanics, School of Science, Wuhan University of Technology, Wuhan, 430070
  • 2School of Undergraduate Education, Shenzhen Polytechnic University, Shenzhen, 518885
出版时间: 2024-10-25 doi: 10.19636/j.cnki.cjsm42-1250/o3.2024.020
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摘要
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为了研究表面形貌对增材制造材料力学性能的影响，本文通过选择性激光熔化方法制备了高强度铝合金试样，研究了扫描速度、热处理、沉积方向、表面粗糙度等对拉伸力学性能的影响，并基于傅里叶级数和MATLABA软件对光学显微镜测量的表面形貌进行了重构，使用Airy应力函数推导获得了表面形貌应力集中系数的解析解. 采用ABAQUS软件进行了有限元分析，对解析结果进行了验证. 通过正态拟合得到应力集中系数的概率密度函数，提出了一种基于屈服强度评估材料可靠性的方法. 本文所提出方法流程为增材制造其他材料及试样表面粗糙度定量化及其对屈服强度影响具有参考意义.

增材制造  /  应力集中系数  /  可靠性分析  /  表面形貌  /  仿真模拟

To investigate the impact of surface topography on the mechanical properties of additive manufacturing materials, in this paper, high-strength aluminum alloy specimens were fabricated by the selective laser melting method. The influences of scanning speed, heat treatment, deposition direction, and surface roughness on tensile mechanical properties were examined. The surface topography measured by an optical microscope was reconstructed based on the Fourier series and MATLAB software, and the analytical solution of the stress concentration coefficient of the surface topography was derived using the Airy stress function. Finite element analysis was conducted using ABAQUS software to validate the analytical results. The probability density function of the stress concentration coefficient was obtained through normal fitting, and a method for evaluating the reliability of the material based on yield strength was proposed. The proposed methodology in this paper is of reference significance for the quantification of surface roughness and its effect on yield strength of other additive manufacturing materials and specimens.

additive manufacturing  /  stress concentration factor  /  reliability analysis  /  surface topography  /  simulation modeling
董子良, 程正坤, 张晓楠, 文聘. 增材制造高强铝合金表面形貌重构及其屈服强度影响规律探究. 固体力学学报, 2024 , 45 (5) : 638 -651 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2024.020
Ziliang Dong, Zhengkun Cheng, Xiaonan Zhang, Pin Wen. Investigation on the Influence of Surface Topography Reconstruction and Yield Strength of High-strength Aluminum Alloys in Additive Manufacturing[J]. Chinese Journal of Solid Mechanics, 2024 , 45 (5) : 638 -651 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2024.020
正文
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0　引言
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金属增材制造技术制备的材料会产生一些会对力学性能产生不利影响的缺陷[1]，例如气泡、成件的表面粗糙度、残余应力或其他因素[2]. 由于应力集中和裂纹萌生，打印部件的力学性能可能会劣化，在这些因素中，表面粗糙度是对3D打印部件力学性能产生影响的主要因素. 其中，Chaus等[3]研究了增材制造17-4ph不锈钢激光表面硼碳合金化的最终组织演变，讨论了表面形貌与粗糙度对合金化的影响. 同时，还有很多文献指出，表面粗糙度对于Mo合金[4]、钛合金[5]、6061铝合金[6]等材料的力学性能都有不同程度的影响. 为此，很多学者不断寻求能够尽可能减小表面粗糙度对材料性能影响的方法，通过参数优化[7]、后处理[8]等方法，尽可能地去消除表面粗糙. 虽然参数优化和后处理可以在一定程度上降低缺陷水平，减小表面缺陷对于性能的影响，但没有有效的方法可以完全消除缺陷，于是学者们开始研究表面粗糙度在工作状态下对其他性能的影响，以及考虑表面粗糙度时粗糙度对于增材制造材料性能的影响规律，主要通过调整工艺参数或进行不同规格的后处理[6,9]，设立对照试验来探究粗糙度对于材料力学性能的影响.
一般情况下，材料的强度随表面粗糙度等级的增加而降低. 表面形貌对力学性能的影响主要是由于表面形貌产生的应力集中. 由于表面形貌的原因，固体表面的应力通常表现为不均匀分布. 这种应力不均匀性的特点是表面形貌峰值处应力较小，而谷值处应力较大. 在加载过程中，由于表面形貌引起的应力集中往往会影响材料表面的稳定性，如疲劳失效、耐蚀性降低等. 由零件表面疲劳裂纹萌生引起的事故占绝大多数[10]，包括零件表面粗糙度过大导致的疲劳断裂失效[11]. 国内外学者基于线弹性理论，分析了加工表面形貌引起的应力集中系数. 在解析求解由表面形貌引起的应力集中系数方面，Srolovitz[12]基于Airy应力函数以一阶精度得到了微扰动正弦表面的应力场分布. Gao[13]基于复变函数和格林函数的思想，以一阶精度得到了微扰动正弦波表面的应力集中系数. 然而，求解增材制造表面形貌引起的应力集中现象对材料本身性能的影响量化方面有所不足，国内外学者只是提出了应力集中现象的求解方式以及应力场的分布规律，对于材料本身性能影响的量化与分析并未深入研究. 本文拟提出一种基于概率论的方式来对材料的拉伸性能进行分析.
本研究针对表面形貌拟采用3D轮廓仪来检测加工产生的表面形貌，对表面形貌进行分类与定量，在这方面，国内外很多学者有着不同的方法. Chen等[14]使用Ra、Rq和Rsk来区分成型样品的上下表面. Fayazfa等[15]基于亚循环疲劳裂纹扩展模型. 将基于表面粗糙度的应力集中因子和缺口试件的渐近应力强度因子插值法扩展了所建立的FCG模型，提出了将表面粗糙度近似为具有与表面不规则性相同应力集中的等效缺口的模型. Iteney等[16]提出一种名为PYROUGH的PYTHON程序，依赖于经典的粗糙度理论，集成了自仿射表面的概念. 实现了几种具有自仿射表面凹凸的基本形状，包括基本块、球体、颗粒和纤维，程序的面向对象结构简化了更复杂对象的实现.
为了尽量避免和减少一些例如机械性能下降、疲劳强度降低和尺寸精度降低等不利影响，更为精确地预测表面粗糙度对力学性能的影响，本文拟采用试验与仿真结合的方法，通过统计学方法以及强度-应力干涉模型来将增材制造过程中产生的表面粗糙度纳入考虑，使得材料的表面形貌对材料力学性能的影响可以一定程度上具有可预测性，从而在已知增材制造各种条件时，预测材料是否满足当前工况. 但是增材制造过程中产生的缺陷并非仅有表面粗糙度，本文着重研究粗糙度对材料拉伸性能造成的影响.
1　材料工艺及实验方法
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1.1　材料的制备
本文试验采用的试样总长度约20 mm，宽度为3 mm，在整体的分析过程中，由于长度远大于宽度，所以整体研究可以看作二维线性问题，在二维维度上，各截面表面粗糙度曲线类似，对其表面取表面粗糙度时取一维表面形貌进行分析.
本实验使用3D金属打印机进行打印，增材制造材料选择Al-Mg-Sc高强铝合金材料，实验用基体为直径50 mm的7075铝合金，使用化学成分Al-5Mg-0.5Sc-0.9Mn-0.35Zr-Si-0.6Ti-0.5Cu-0.25Cr（wt. %）的合金粉末为原材料进行制备，使用的激光熔化沉积设备为LDF3000-40型号（中国航空工业集团公司北京航空材料研究院3D打印研究与工程技术中心）. 其原理及材料粉末的粒径如图1所示，通过激光粒度仪对粉末粒度分布进行了测试，结果如图1所示：D10：44.26 μm，D50：74.39 μm，D90：116.72 μm. 使用图像法对粉末球形度进行了测量，粉末球形度为0.78. 增材制造的基材如图1（c）所示.
为了研究不同工艺对于材料表面粗糙度和材料力学性能的影响，本文控制激光功率在1500w，扫描速率梯度递增，同时对制备出的材料进行退火热处理作为对照，来分析退火热处理对于材料的表面粗糙度与力学性能的影响，具体工艺参数如表1所示.
图2为扫描速率为500 mm/s、600 mm/s和700 mm/s时制造的材料的成分分布. 图像的结果表明，扫描速率对材料成分的分布产生一定影响. 由图2可以看出增加扫描速率可以减少材料表面的偏积，进而提高材料的力学性能.
相邻的沉积层重叠50%，粉末给料速率为7.6 g/min，单层沉积的厚度约为0.5 mm，共沉积了10层，总沉积厚度约为4 mm. 沉积沿着7075铝合金基体的轴向进行，沉积长度为50 mm. 为防止样品氧化，制备过程在氩气氛围中进行. 为了研究不同工艺参数对材料表面粗糙度的影响，使用不同工艺制备了不同的基材. 同时，从每个基材中切割出若干相同尺寸的拉伸试样进行力学性能测试. 拉伸试样从增材制造样品中切割，规格为如图3所示的非标拉伸试样.
1.2　实验方法及结果分析
拉伸试验在室温下采用固定加载速率为0.1 mm/min的万能材料试验机进行. 每组工艺参数切割了3-4个试样进行实验，原粗糙试样厚度约为2 mm，打磨抛光至厚度为1.2 mm，测试其拉伸应力应变曲线，计算杨氏模量、泊松比和屈服强度等力学性能. 为了排除增材制造带来的性能各向异性问题，本次实验除下列组别之外，还额外在400 mm/s扫描速率条件下制备了一块基材，分别沿堆叠方向与扫描方向进行试样切割处非标拉伸试样并以同样的条件进行拉伸试验，对拉伸试验应力-应变曲线起点处作切线，计算其斜率，得到等效杨氏模量结果如表2所示.
表2的结果证明了本文材料在当前环境下制备的材料各向异性差距可以忽略不计.
除了光滑的试样外，每组还添加了2-3个未经抛光的试样，在相同条件下进行拉伸测试，未经抛光的试样厚度约为2±0.5 mm. 加载速率均为0.1 mm/min，近似准静态拉伸条件. 两种拉伸试样的表面形貌对比如图3所示. 拉伸试验的结果如表2所示，拉伸试验的数据图如图5所示，其中，700 mm/s为未经热处理的材料，700 mm/s（h）为热处理之后的材料，热处理的工艺类型为退火热处理，加热温度为360 ℃，加热时长8 h.
根据表3与图4不难看出，随着扫描速率的提升，材料在拉伸时的力学性能也会逐步提升，700 mm/s扫描速率下的材料拉伸力学性能最好，对比500 mm/s扫描速率下的材料，抗拉强度提升了12.6%，屈服强度提升了8.7%，断后延展率提升了33.3%. 热处理对于材料的抗拉强度与屈服强度有所提升，对比未经热处理的材料而言，其抗拉强度和屈服强度分别提升了12.2%和28.0%，材料的延展性相对未热处理的材料降低了29.4%，这是因为热处理会改变位错密度，导致材料断裂韧性降低，从而使得断后延长率降低[17]. 粗糙试样屈服强度分别下降6.22%、6.68%、7.08%、7.67%.
同时测试拉伸试样的断口形貌如图5所示. 由断面推断，整体材料分布均匀，中心位置与边缘位置致密度、成型质量差别可忽略不计，证明本文拉伸实验所体现的性能差距与成型之后的孔隙度无关，拉伸试样断口较为平滑，有一定颈缩.
粗糙与光滑的各组材料应力应变曲线对比如图6所示，对比四组试样的应力应变曲线，发现对于粗糙试样来说，屈服极限来得更早，屈服现象更加明显，抗拉强度普遍降低，本文认为这种现象是由于材料表面粗糙度的存在而导致的，故本文从表面粗糙度入手，研究材料表面粗糙度对材料力学性能的影响. 本文将针对增材制造材料表面粗糙度引起应力集中、进而影响材料屈服强度进行研究并作出讨论.
2　表面形貌重构及应力集中系数求解
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2.1　表面形貌测量
本研究中使用的测试样本总长度约为8 mm，宽度为2.5 mm. 在整体分析过程中，由于长度远大于宽度，整个研究可被视为一个二维线性问题. 在二维维度中，各横截面表面的粗糙度曲线相似. 在考虑表面粗糙度时，进行一维表面剖面的分析. 本实验中的表面形貌数据使用3D光学显微镜（型号：VHX-7100）进行采集. 所使用的形貌提取分析软件为机器配套软件Professional 3D，实验所得表面形貌数据如图8所示.
试样整体呈现出一些凸起和凹陷，但表面上没有明显的颗粒物，只有轻微的波动，所以对材料力学性能的主要影响因素为材料表面形貌引起的应力集中，本文将根据材料的表面形貌来研究表面应力集中对于材料的力学性能的影响.
通过图像扫描结果来看，表面粗糙的程度有随着扫描速率增加而先降低后升高的趋势，热处理也会增加表面的粗糙程度，而表面粗糙度的改变会造成表面应力集中现象的改变.
2.2　表面形貌重构
增材制造表面形貌的形成可以被视为经历各种状态的平稳随机过程. 可以通过提取不同阶次表面形态谐波的振幅、频率和相位信息，然后使用谐波叠加方法来模拟它[18]. 表面形态可以拟合为：
选取本文600 mm/s扫描速率制备的拉伸试样进行表面的谐波叠加模拟. 将数据导入程序并进行快速傅里叶变换（Fast Fourier Transform，FFT）后，可以提取每个阶次的振幅、频率和相位角，根据公式1计算的各阶次振幅、频率和相位按照谐波叠加的方法进行叠加，模拟材料的表面形貌. 结果如图8所示，实线为实测表面形貌，虚线为谐波叠加表面形貌.
图示叠加效果良好，引入本文拉伸试样时，采样长度设置为L=4 mm，采样间隔为0.0005 mm，分别对四组材料实测表面形貌进行谐波叠加模拟表面形貌.
2.3　应力集中系数解析解
在实际实验中，材料的表面形态可以看作是由平坦表面产生的扰动. 这里的轮廓被表示为函数f（x），其在其定义域内满足傅里叶变换条件. 轮廓f（x）可以通过使用傅里叶变换叠加多个余弦分量来描述. 在本节的讨论中，假设表面上所有点的斜率都非常小. 对于波动表面，必须强制执行的边界条件是牵引力为零. 如果应力场对应于表面上的一个点并且位于外部单位法线方向上，则边界条件为0. 在外部载荷作用下，表面层附近的应力分量将受到表面扰动的影响，在受扰动的表面轮廓底部将发生应力集中，而在波峰处应力会减小. 表面层附近的应力分量可以表示为受扰动表面的应力场形式[19]，对于余弦扰动和均匀的初始应力场，应力函数需要满足双调和方程，以确保平面应力场既满足应力平衡微分方程又满足变形协调方程. 应力场应该表现出适当的对称性，并且可以用线性弹性理论中用于解决二维问题的常用Airy应力函数表示. 在一阶准确度的情况下，通过逐个扰动每个谐波分量在叠加表面形貌上引起的附加应力分量满足叠加原理，即逐个扰动每个谐波分量引起的附加应力分量的总和. 谐波叠加表面形态的应力沿深度方向呈指数衰减，衰减指数仅与每个谐波的波长有关. 谐波叠加表面形貌的应力集中系数[18]为：
根据公式叠加之后的应力集中系数是一条完整连续的曲线，线上每一个点都对应着材料表面一点的应力集中系数，如图9所示，横坐标为材料长度x，纵坐标为应力集中系数数值. 由应力集中曲线图也可以验证扫描速率和表面粗糙度的关系.
2.4　应力集中系数解析解及拉伸试验的有限元验证
本文所研究问题可以看作二维的平面应力问题，由于表面粗糙度的量级与材料本身大小差异较大，如果划分传统四边形网格会导致网格数量巨大，为了在不影响结果的条件下缩减计算时长，采用三合一网格进行层层递进地网格划分.
模型采用长度为2 mm，宽度为1 mm的长方形模型，本文粗糙试样表面形貌扫描长度为2 mm，试样厚度为2 mm，给予模型下边界y方向位移为0，右侧边界x方向位移为0，左侧边界给予位移载荷进行拉伸，边界条件与载荷这样设计的原因是因为该模型是取实际拉伸试样四分之一进行仿真.
通过读取600 mm/s扫描速率材料表面粗糙度数据，对模型提取出来的节点进行改变，使得材料上层网格拟合为真实的材料表面形貌，读取inp文件进行作业，从结果的应力云图上来看，应力出现不均匀的分布，峰值处应力较小，谷值处应力较大. 在可视化模块中提取表面一层节点的应力情况进行计算，得出相应点的应力集中系数绘制成曲线，与应力集中系数解析解对比结果如图11所示.
从结果图像上看，解析解的可行性得到了有限元解的验证，计算结果可以直接应用.
拉伸仿真计算时，对本文的拉伸试验进行验证，对材料的粗糙模型进行分析，同时使用未进行表面形貌模拟的光滑模型进行同条件的拉伸仿真，输出宏观模型应力-应变曲线，所使用材料属性为600 mm/s扫描速率下制备样品的几何形貌和材料属性，载荷设置为模型下边界y方向位移为0，右侧边界x方向位移为0，左侧给予位移载荷进行拉伸，分析并输出模型的应力和应变. 两种模型仿真应力结果如图12所示.
仿真输出应力-应变曲线如图13所示，光滑模型的屈服强度为151.7 MPa，粗糙模型的屈服强度为142.2 MPa，仿真结果与实验结果较为吻合. 仿真结果对比实验结果，在弹性阶段与屈服点处略高，这是由于试样内部存在一定气孔或其他影响拉伸性能的因素，而在弹性阶段之后，实验结果斜率逐渐变小，并且结果略高于仿真结果，这是由于本文材料采用理想双线性弹塑性材料本构模型，在塑性阶段存在波动偏差. 通过观察屈服点，发现粗糙试样的有限元仿真与实验结果几乎相同，转折点出现在曲线的同一位置. 对比光滑模型与粗糙模型的性能差异，实验数据表明屈服强度下降约6.68%，仿真结果显示屈服强度下降约6.26%，实验数据与仿真数据有误差是由于材料的拉伸性能影响因素并非只有粗糙度，内部存在一定气孔或其他影响拉伸性能的因素.
3　考虑表面粗糙度的材料屈服强度
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3.1　表面粗糙度的量化统计
可靠性可以通过外部应力与工件固有强度之间的关系来表达. 由于在增材制造中由各种因素引起的变化，工件的固有强度呈现统计分布. 同样，产品将经历的应力由于不同的操作条件也呈现统计分布. 当这两个分布重叠时，产品失效. 从概率的角度来看，产品的固有强度与外部应力之间的差距越大，可靠性越高，反之亦然. 在整个打印过程中，每个工艺参数都可能以不同程度影响材料的可靠性. 虽然在准静态问题中这种影响可能不太明显，在循环加载条件下，安全系数被放大，加速了工件的疲劳. 针对这种情况，本文提出使用统计方法研究应力集中系数对材料可靠性的影响.
如果需要确定每个小区域的强度变化模式，在实际的打印过程中，强度的变化模式并不遵循线性分布. 相反，由于打印过程中的各种随机干扰因素，整个强度范围内的强度呈现随机分布. 由于增材制造过程中的每个粉末喷射都可以视为具有相似分布的独立随机变量，根据中心极限定理，整体表面形态趋向于遵循正态分布. 在整体材料上，这表现为缺陷位置的不可控，但缺陷大小在可控范围内，在材料表面，凹陷和凸起也大致遵循正态分布. 本文通过提取研究的金属增材制造组件的扫描和重构得到的表面形貌曲线数据来计算应力集中系数，通过应力集中系数数据进行计算，验证了扫描速率为600 mm/s的材料表面的应力集中系数数据分布图像符合正态分布，结果如图14所示.
3.2　基于正态分布分析考虑表面粗糙度的可靠性分析方法
本文假设应力集中系数遵循正态分布，其概率密度函数如下：
记作X～N（μ，σ2）.
对应的概率密度分布函数是：
其中均值μ与标准差σ如表3所示. 由于材料应力集中系数遵循正态分布，所以使用正态分布函数常用统计常数μ+σ、μ+2σ、μ+3σ来进行材料光滑和粗糙试样屈服强度的折算，计算结果见表4.
表4的数据中，负数表示该处受压. 从表4中可以观察到，在相同的激光功率下，尽管提高打印速度增强了材料的强度，但增加打印速度会使得表面粗糙程度先降低后升高. 同时还发现，经过退火热处理的组别表现出比未经处理的样本明显更高的表面粗糙度，应力集中引起的扰动应力较大，这是因为退火热处理会使得未完全熔融的粉末进一步熔融，铝合金内部晶粒重组，导致粗糙度提升[20]. 但热处理对表面粗糙度的影响很有限，一般只用作提高材料的强度、刚度等性能. 计算全组别表面应力集中系数的概率函数，得到平均值，采用线性回归的方式对表面应力集中系数与打磨前后的屈服强度进行拟合，得到公式（5）：
折算验算结果如表5所示：
材料的屈服强度也可以用公式（5）来大致推断，但由于金属材料具有延展性，所以在材料在拉伸过程中会发生变形，材料整体会变长，每两个缺陷之间的距离也会逐步增加，并在整个塑性阶段都会持续产生这种变化，基于材料原本表面形貌计算的应力集中系数将不再适用，所以对于材料塑性阶段力学性能及抗拉强度的评估，是本文研究不足的地方.
4　结论
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本文深入探讨了金属增材制造在不同打印速率和热处理条件下，表面粗糙度对应力集中、材料可靠性和疲劳特性的影响. 利用理论推导、有限元分析和统计方法，本文旨在全面了解金属增材制造中表面效应的复杂机制，为材料工程领域的工程师和研究人员提供有价值的见解.
（1）表面形貌产生的应力集中系数解析解的应用：本文引用了由于表面形貌引起的应力集中系数解析解. 利用傅里叶分析，表面形貌被重构为多个余弦分量的叠加. 把应力集中系数解析解从理论引用到实际应用，并在后续验证了其可行性.
（2）通过有限元分析验证解析解的准确性：通过有限元分析验证了解析解的准确性. 采用ABAQUS商业软件，使用三合一网格对二维平面拉伸问题进行建模. 解析解和有限元解的比较显示出强烈的相关性，验证了解析方法的有效性和实用性. 这一步为进一步研究提供了可靠的数值验证方法.
（3）探索应力集中系数对材料可靠性的影响：本文引入正态分布模型，研究应力集中系数对材料屈服强度的影响. 通过统计分析，检验了在不同打印速率和热处理条件下材料强度的分布. 利用正态分布模型，计算了应力集中系数的概率密度分布. 这种方法使研究人员能够全面了解不同条件下材料的屈服强度折算，为工程实践提供了可行的评估框架.
总之，本文通过理论推导、有限元分析和统计方法深入研究了金属增材制造的表面效应. 研究结果不仅为提高材料可靠性和优化工艺参数提供了指导，还为材料工程领域的研究提供了强有力的支持. 未来的研究方向可能包括进一步优化解析解，并更深入地探讨表面效应对材料疲劳特性的影响，为材料工程的进展提供有价值的见解.
基金
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  • 国家自然科学基金项目(11902232)
  • 广东省基础与应用基础研究基金海上风电联合项目(2022A1515240057)
  • 深圳市科技计划项目(20231128093312001)
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2024年第45卷第5期
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doi: 10.19636/j.cnki.cjsm42-1250/o3.2024.020
  • 接收时间：2024-05-24
  • 首发时间：2026-04-01
  • 出版时间：2024-10-25
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  • 收稿日期：2024-05-24
基金
国家自然科学基金项目(11902232)
广东省基础与应用基础研究基金海上风电联合项目(2022A1515240057)
深圳市科技计划项目(20231128093312001)
作者信息
    1武汉理工大学理学院工程结构与力学系，武汉，430070
    2深圳职业技术大学本科教育学院，深圳，518885

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2种不同金属材料的力学参数
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
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