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Article(id=1243220385735491682, tenantId=1146029695717560320, journalId=1242844143416819734, issueId=1243220377556595432, articleNumber=null, orderNo=null, doi=10.15959/j.cnki.0254-0053.2025.03.020, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1738512000000, receivedDateStr=2025-02-03, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774336437876, onlineDateStr=2026-03-24, pubDate=1758729600000, pubDateStr=2025-09-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774336437876, onlineIssueDateStr=2026-03-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774336437876, creator=13701087609, updateTime=1774336437876, updator=13701087609, issue=Issue{id=1243220377556595432, tenantId=1146029695717560320, journalId=1242844143416819734, year='2025', volume='46', issue='3', pageStart='541', pageEnd='810', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774336435926, creator=13701087609, updateTime=1774336648182, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1243221267898282005, tenantId=1146029695717560320, journalId=1242844143416819734, issueId=1243220377556595432, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1243221267898282006, tenantId=1146029695717560320, journalId=1242844143416819734, issueId=1243220377556595432, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=802, endPage=810, ext={EN=ArticleExt(id=1243220385941012585, articleId=1243220385735491682, tenantId=1146029695717560320, journalId=1242844143416819734, language=EN, title=A Modified Test Method and Formula for Tensile Fracture Toughness of Putty, columnId=null, journalTitle=Chinese Quarterly of Mechanics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Due to the low strength of putty, it is impossible to directly measure its fracture toughness using the standard tensile fracture test. In order to accurately measure the tensile fracture toughness of low-strength materials such as putty, this study presents an improved compact tension test method and derives a tensile fracture toughness formula through numerical analysis. The formula is further refined by accounting for boundary effects, and its accuracy is validated through systematic testing with varying initial crack lengths. The results demonstrate that, the modified formula enables direct calculation of material fracture toughness. The stress intensity factor depends on relative boundary conditions rather than absolute boundary effects, with boundary effects becoming more pronounced with increasing initial crack length. The specimens exhibit pure Mode I fracture, with the modified formula yielding a stable fracture toughness of approximately 42 kN/m3/2. Experimental validation confirms the accuracy of both the improved test method and the modified formula, establishing their applicability for measuring fracture toughness in low-strength materials like putty and contributing to putty material development.

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由于腻子强度低，无法直接采用标准张拉断裂试验测试其断裂韧性．为了较为准确地测试出腻子等低强度材料的张拉断裂韧性，本文对紧凑拉伸试验进行改进，结合数值方法推导出了张拉断裂韧性的计算公式，并基于边界效应的影响对公式进行了修正．之后采用不同初始裂缝长度的紧凑拉伸试验，对修正公式的准确性进行验证．研究结果表明：修正公式可以直接计算出材料的断裂韧性；应力强度因子与有限边界效应无关，与相对边界条件有关，且随着初始裂缝增大，边界效应越明显；试样的断裂符合张开型断裂形式，基于修正公式求出的断裂韧性约为42 kN/m3/2，且波动较小；通过试验验证了改进后试验方法及修正公式的准确性，研究成果可用于腻子等低强度材料断裂韧性的测试，对腻子的研发及升级迭代具有指导意义．

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朱林．E-mail：
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朱林，讲师，硕士．研究方向：岩土工程．

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朱林，讲师，硕士．研究方向：岩土工程．

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朱林，讲师，硕士．研究方向：岩土工程．

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figureFileBig=RE2vOhLAtJSWHKxs4cqQLw==, tableContent=null), ArticleFig(id=1243220404882489999, tenantId=1146029695717560320, journalId=1242844143416819734, articleId=1243220385735491682, language=CN, label=图12, caption=断裂韧性计算公式修正前后对比, figureFileSmall=eYIwY5WUR5Z4IcuNDmI3yA==, figureFileBig=RE2vOhLAtJSWHKxs4cqQLw==, tableContent=null), ArticleFig(id=1243220404962181783, tenantId=1146029695717560320, journalId=1242844143416819734, articleId=1243220385735491682, language=EN, label=Tab.1, caption=

Comparison of crack tip stress with different seam height ratios

, figureFileSmall=null, figureFileBig=null, tableContent=
Seam height ratio a/bCrack depth a/cmCrack tip stress σy/kPaStress intensityh factor KI/(kN/m3/2)
0.152.0232.436.8
0.223.0310.449.2
0.304.0403.463.9
0.375.0517.782.1
0.456.0662.1105.0
0.537.0855.7135.6
0.608.01 126.3178.6
0.648.51 307.7207.3
0.739.71 943.8308.2
0.7910.52 629.7416.9
), ArticleFig(id=1243220405088010912, tenantId=1146029695717560320, journalId=1242844143416819734, articleId=1243220385735491682, language=CN, label=表1, caption=

不同缝高比裂尖应力对比表

, figureFileSmall=null, figureFileBig=null, tableContent=
Seam height ratio a/bCrack depth a/cmCrack tip stress σy/kPaStress intensityh factor KI/(kN/m3/2)
0.152.0232.436.8
0.223.0310.449.2
0.304.0403.463.9
0.375.0517.782.1
0.456.0662.1105.0
0.537.0855.7135.6
0.608.01 126.3178.6
0.648.51 307.7207.3
0.739.71 943.8308.2
0.7910.52 629.7416.9
), ArticleFig(id=1243220405289337514, tenantId=1146029695717560320, journalId=1242844143416819734, articleId=1243220385735491682, language=EN, label=Tab.2, caption=

Fracture toughness test results

, figureFileSmall=null, figureFileBig=null, tableContent=
Crack depth a/cmSpecimen height B/cmCoefficient YTensile breaking stress σ/kPaFracture toughness KIC/kN/m32
3142.8387.0542.66
4143.0668.5141.91
5143.4055.7042.41
6143.9342.4340.82
7144.7233.6141.94
8145.9124.8241.47
), ArticleFig(id=1243220405410972340, tenantId=1146029695717560320, journalId=1242844143416819734, articleId=1243220385735491682, language=CN, label=表2, caption=

断裂韧性试验测定结果

, figureFileSmall=null, figureFileBig=null, tableContent=
Crack depth a/cmSpecimen height B/cmCoefficient YTensile breaking stress σ/kPaFracture toughness KIC/kN/m32
3142.8387.0542.66
4143.0668.5141.91
5143.4055.7042.41
6143.9342.4340.82
7144.7233.6141.94
8145.9124.8241.47
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腻子张拉断裂韧性测试方法改进及计算公式修正
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朱林 1, 2 , 刘子苑 1, 2 , 王滕 3
力学季刊 | 2025,46(3): 802-810
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力学季刊 | 2025, 46(3): 802-810
腻子张拉断裂韧性测试方法改进及计算公式修正
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朱林1, 2 , 刘子苑1, 2, 王滕3
作者信息
  • 1.河北水利电力学院　土木工程系，河北　沧州　061001
  • 2.河北省岩土工程安全与变形控制重点实验室（河北水利电力学院），河北　沧州　061001
  • 3.北京交通大学　土木建筑工程学院，北京　100010

    • 朱林，讲师，硕士．研究方向：岩土工程．

通讯作者:

朱林．E-mail：
A Modified Test Method and Formula for Tensile Fracture Toughness of Putty
Lin ZHU1, 2 , Ziyuan LIU1, 2, Teng WANG3
Affiliations
  • 1.Department of Civil Engineering, Hebei University of Water Resources and Electric Engineering, Cangzhou 061001, Hebei, China
  • 2.Key Laboratory of Geotechnical Engineering Safety and Deformation Control (Hebei University of Water Resources and Electric Engineering), Cangzhou 061001, Hebei, China
  • 3.School of Civil Engineering, Beijing Jiaotong University, Beijing 10010, China
出版时间: 2025-09-25 doi: 10.15959/j.cnki.0254-0053.2025.03.020
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由于腻子强度低，无法直接采用标准张拉断裂试验测试其断裂韧性．为了较为准确地测试出腻子等低强度材料的张拉断裂韧性，本文对紧凑拉伸试验进行改进，结合数值方法推导出了张拉断裂韧性的计算公式，并基于边界效应的影响对公式进行了修正．之后采用不同初始裂缝长度的紧凑拉伸试验，对修正公式的准确性进行验证．研究结果表明：修正公式可以直接计算出材料的断裂韧性；应力强度因子与有限边界效应无关，与相对边界条件有关，且随着初始裂缝增大，边界效应越明显；试样的断裂符合张开型断裂形式，基于修正公式求出的断裂韧性约为42 kN/m3/2，且波动较小；通过试验验证了改进后试验方法及修正公式的准确性，研究成果可用于腻子等低强度材料断裂韧性的测试，对腻子的研发及升级迭代具有指导意义．

腻子  /  张拉断裂  /  断裂韧性  /  应力强度因子  /  张拉断裂试验

Due to the low strength of putty, it is impossible to directly measure its fracture toughness using the standard tensile fracture test. In order to accurately measure the tensile fracture toughness of low-strength materials such as putty, this study presents an improved compact tension test method and derives a tensile fracture toughness formula through numerical analysis. The formula is further refined by accounting for boundary effects, and its accuracy is validated through systematic testing with varying initial crack lengths. The results demonstrate that, the modified formula enables direct calculation of material fracture toughness. The stress intensity factor depends on relative boundary conditions rather than absolute boundary effects, with boundary effects becoming more pronounced with increasing initial crack length. The specimens exhibit pure Mode I fracture, with the modified formula yielding a stable fracture toughness of approximately 42 kN/m3/2. Experimental validation confirms the accuracy of both the improved test method and the modified formula, establishing their applicability for measuring fracture toughness in low-strength materials like putty and contributing to putty material development.

putty  /  tension fracture  /  non-stationary  /  stress intensity factor  /  tensile fracture test
朱林, 刘子苑, 王滕. 腻子张拉断裂韧性测试方法改进及计算公式修正. 力学季刊, 2025 , 46 (3) : 802 -810 . DOI: 10.15959/j.cnki.0254-0053.2025.03.020
Lin ZHU, Ziyuan LIU, Teng WANG. A Modified Test Method and Formula for Tensile Fracture Toughness of Putty[J]. Chinese Quarterly of Mechanics, 2025 , 46 (3) : 802 -810 . DOI: 10.15959/j.cnki.0254-0053.2025.03.020
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在对墙面进行涂料装饰时，通常先在基层上涂抹一层腻子找平，从而便于涂料涂刷[1-3]．然而，在环境温度和湿度的长期变化影响下，腻子容易发生开裂，导致外层涂料的开裂、脱落和漏水等问题[4-5]．腻子抗开裂能力的研究对预防开裂具有重要意义，其中断裂韧性是表征腻子抗开裂能力的主要指标．因此，准确测量腻子的断裂韧性是判断腻子耐久性的前提．
腻子开裂属于脆性材料断裂力学的范畴，在过往数十年中，脆性材料断裂的研究多集中在岩石、混凝土等高强度材料．对于高强度材料断裂韧性的测试主要有三点弯曲试验[6]与紧凑拉伸试验[7]两种方法，但对于低强度材料，由于制样过程中容易造成初始损失，无法直接应用上述两种方法．对于低强度材料断裂的研究主要集中在岩土工程中的硬土或者超固结土．以往研究[8]认为基于断裂力学对土体破坏进行研究非常适用．如Saada等[9]首次对土体断裂参数进行了测试，但是操作过程较为复杂，且具有争议性．之后，Lee等[10]采用紧凑拉伸试验对粘土的Ⅰ型断裂能释放率Gc进行了测试，但是该方法容易在加载点先发生破坏．Harison[11]采用环试验对粘土断裂参数进行了测试，但操作也较为复杂．Chandler[12]采用三点弯曲断裂试验对粘土断裂参数进行了测试，该方法受材料自重影响较大．胡骏峰[13]采用改进后的三点弯曲试验对压实粘性土Ⅰ-Ⅱ复合型断裂特性进行了研究，但该方法试验误差较大，尤其对于低强度材料，结果离散程度较高．丁金粟等[14]对紧凑拉伸试验进行了改进，实现了软粘土张拉断裂韧性的测试，且结果较为稳定．对于腻子强度的研究相对较少，采用哑铃型试件单轴加载，可测定抗拉强度，但该方法试样难以成型，且拉断难以实现[15]．还有学者采用数字图像相关（Digital Image Correlation，DIC）技术进行测试，但是该方法实现困难，成本高[16-17]．由于腻子强度较低且开裂时主要为张拉断裂，可以对紧凑拉伸试验进行改进，从而用于腻子张拉断裂韧性的测试．
本文对紧凑拉伸试验进行了改进，推导了张拉断裂韧性的计算公式，并基于边界效应的影响对公式进行了修正，之后采用不同初始裂缝长度的紧凑拉伸试验，对修正公式的准确性进行验证，从而证明改进后测试方法的可行性及计算公式的准确性，研究工作对腻子的研发和升级迭代具有指导意义．
1　张拉试验方法改进
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1.1　标准紧凑拉伸试验
在含裂纹体承受载荷时，裂纹尖端附近的应力场呈现复杂的三维分布．基于线弹性断裂力学理论，可将该应力场在裂纹局部坐标系下分解为三个相互独立的应力分量，分别对应于三种基本的裂纹张开模式．I型（张开型）：裂纹面受到垂直于裂纹平面的法向拉应力作用，裂纹面内无剪切应力分量．裂纹的扩展表现为垂直于裂纹面的纯张拉破坏．Ⅱ型（滑开型）：裂纹面受到作用在裂纹平面内、且垂直于裂纹前缘方向的剪应力作用．裂纹的扩展主要由面内剪切主导，表现为剪切破坏．Ⅲ型（撕开型）：裂纹面受到作用在裂纹平面内、但平行于裂纹前缘方向的剪应力作用．裂纹的扩展同样由剪切机制控制，表现为面外剪切破坏．这三种基本模式构成了分析复杂裂纹问题的理论基础，实际工程中的裂纹扩展往往是这些基本模式的线性叠加，如图1所示．
由于腻子破坏时主要为张拉破坏，在腻子性能评价指标中仅对抗拉拔强度进行了规定．为了方便测得腻子的抗拉拔强度，有必要对拉拔试验测试方法进行研究．腻子拉拔破坏为张开型破坏．国标[18]给出了标准紧凑拉伸试验方法，在试样两侧设置张拉孔，并施加张拉荷载，如图2所示，材料的张拉断裂韧性可由下式求得
式中，KIC为断裂韧性，E为弹性模量，P为荷载，其余为尺寸参量，具体见图2．
1.2　紧凑拉伸试验改进
标准紧凑拉伸试样在测试腻子类低强度材料断裂韧性时存在显著局限性．该类材料的固有低抗拉强度导致预制裂纹孔（加载孔）处产生显著的应力集中效应，极易引发孔边过早失效或非预期破坏．该失效模式常发生于孔壁区域，而非预制裂纹尖端，从而严重干扰裂纹的稳定起裂与扩展过程．因此，标准CT试验方法无法有效准确地表征腻子材料的I型断裂韧性．基于此，本文对该方法进行了改进，通过在长方体试样两侧施加均布荷载进行张拉试验，避免了开孔对初始试样的扰动．图3给出了改进后的紧凑拉伸试验设备图，本实验装置设计用于对材料试样实施准静态单轴拉伸测试，并同步监测其载荷-位移响应，具体试验方法如下
（1）试样轴向两端各固接一块刚性钢板作为加载端板．每块端板背侧焊接有高强度拉环．左侧拉环通过钢丝绳与刚性固定立柱耦合，提供约束反力．右侧拉环则通过钢丝绳串联连接至一台高精度拉压式称重传感器．
（2）称重传感器的另一端连接至配重系统，用于向试样施加轴向拉伸载荷．该传感器实时输出与试样所受拉力成正比的电信号．
（3）上述称重传感器通过专用信号线缆与数据采集仪及数字显示屏互联．此系统能够连续、高采样率地记录并显示试样承受的实时拉力数据．
（4）为精确表征试样的轴向变形，在试样标距段两侧对称布置两台高分辨率接触式位移计．通过实时采集并计算这两台位移计读数的差值，可有效消除试样可能的刚体位移影响，从而获得试样在拉伸过程中的净轴向变形量．为最大限度降低试样在加载过程中与支撑台面之间滑动摩擦阻力对测试结果的影响，试样底部被置于一块经特殊处理的低摩擦系数滑板上．
2　断裂韧性计算公式修正
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2.1　基于边界效应影响的公式修正
由于该方法的加载方式有所改变，标准中给定的断裂韧性计算公式不再适用，本节基于断裂力学理论对原计算公式进行修正．考虑一个承受远场双轴均匀拉伸应力场的无限大平板，其中心含有一条长度为2a的穿透性直裂缝，如图4所示．为进行断裂分析，定义两个坐标系：以裂缝中点为原点建立全局直角坐标系（x，y）；以裂缝尖端（通常指右尖端）为极点建立局部极坐标系（γ，θ）．
裂缝尖端的应力场为
式中，σy为全局直角坐标系中应力分量，KI为应力强度因子，量纲为kN/m3/2．σ为平均拉应力，a为初始裂缝长度．
断裂韧性KIC作为材料的本征属性，其理论计算通常基于理想化的无限大板模型，如式（4）所示．该模型将断裂起始与远场名义拉应力直接关联．然而，此模型未考虑实际试样或结构存在的边界条件对裂纹尖端应力场及约束度的影响．因此，直接应用该公式解析实验室有限尺寸试样的断裂试验数据，会因显著的约束损失导致对KIC的高估．为获得更接近材料真实断裂韧性的表征值，必须依据具体的试样构型与加载条件，引入边界修正因子或采用更完善的约束相关断裂力学模型对式（4）进行修正．
为建立应力强度因子KI与裂纹长度a的定量关系，需依据其定义进行求解．如式（4）所示，应力强度因子可由裂纹尖端前方特定位置（θ=0）且距离尖端为r处的渐近应力场分量直接计算得出．然而，裂纹尖端区域存在显著的应力奇异性，其周围应力场分布高度复杂，难以通过经典的弹塑性理论获得精确的解析解．鉴于当前基于有限元法的数值计算技术已高度成熟并广泛应用，该方法是获取裂纹尖端附近高梯度应力分布场的有效手段．因此，针对给定的矩形截面试样，可采用经过收敛性验证的有限元数值模拟，求解裂纹尖端附近目标位置r处的应力分量，进而依据式（4）计算相应的应力强度因子．
模型长l=16 cm，高b=14 cm，采用二维平面应变模型，在试样的几何对称面预制一条长度为a的初始裂纹，并于模型两侧边界施加垂直于裂纹面的远场均匀拉伸应力，其幅值为100 kPa，如图5（a）所示．裂缝长度a取值范围为0.5~11 cm，共计17种工况．裂尖网格加密划分，经过网格敏感性分析，发现裂尖网格尺寸小于0.5 mm时网格对结果精度影响较小，本模型裂尖网格尺寸设置为0.2 mm．图5给出了部分工况的垂直于裂缝方向的应力σy云图．表1给出了设定的缝高比裂尖正前方附近的水平应力以及计算得到的应力强度因子KI．
2.2　有限边界效应影响
断裂力学理论指出，自由边界对裂纹尖端应力场及断裂韧性的影响取决于裂纹长度a与其尖端至最近自由边界的韧带尺寸（b-a）．有限边界效应是指不仅改变初始缝长，而且改变模型的绝对高度．相对边界条件是指初始裂缝长度与试件高度的相对大小，因此将相对边界效应定义为初始裂缝长度a与试件高度b的比值（a/b）．
为了消除有限边界效应的影响，本节采用同样的方法对矩形试样进行张拉模拟，模型长度保持不变l=16 cm，高度b取20 cm、25 cm、30 cm等三种工况，每个高度工况下初始裂缝长度a分别设置了15种工况．其中，高度20 cm工况下不同裂缝长度时裂尖0.4 cm处的应力σy及通过式（4）求得的应力强度因子KI见表1．图6展示了不同模型高度下，应力强度因子KI随缝长高度比（a/b）的变化规律．分析表明，KI值随a/b增大呈显著递增趋势，且其增长率随a/b增大而增加．该现象可归因于：随着a/b增大，裂尖距自由边界的相对距离减小，导致在恒定远场张拉荷载作用下，裂尖应力奇异性增强，从而显著提升了KI的数值．
试验结果表明，在几何尺寸与裂纹长度存在差异，但无量纲裂纹长度（a/h）保持恒定的条件下，应力强度因子呈现高度一致性．该现象表明KI随缝长高度比（a/b）的变化规律几乎不受有限边界效应的影响．
2.3　相对边界效应影响
为了消除相对边界效应的影响，将式（4）改为
式中，Y为与边界相关的无量纲系数．因此，应力强度因子KI受裂纹长度与板高几何参数比（a/b）的影响，可通过无量纲几何形状因子Y予以表征．基于数值计算结合解析方法，可获得不同a/b值所对应的Y值．如图7所示，通过绘制Y随a/b的变化关系曲线，揭示了二者之间的定量关联．对该数据集进行回归分析，建立了描述Y（a/b）关系的数学模型，其表达式为
该拟合模型的相关系数R2=0.998，表明所建立的回归方程具有极高的统计显著性，能够精确表征几何形状因子Y随裂纹尺寸比a/b的变化规律．当a/b小于0.1时，试样不易断裂，试验结果离散较大；当a/b大于0.5时，试样容易产生初始损伤，因此a/b的合理范围为0.1~0.5，材料的断裂韧性可以表示为
式中，KIC表征断裂韧性；a为试样预制初始裂纹的长度；b表示平行于裂纹扩展方向的试样宽度；σC指试样断裂时远场施加的名义拉应力．
3　修正公式的试验验证
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为了验证改进后的紧凑拉伸试验方法的可行性以及修正后应力强度因子计算公式的准确性，本节采用室内试验的方法对其进行验证．图8给出了改进后的试验装置，并依托该装置进行不同缝长高度比的紧凑拉伸试验．
本次试验采用长方体试件，长l=16cm，高b=14 cm，厚W=7 cm，试样采用浇筑法制作，采用切割法预制不同高度的初始裂缝，如图9所示．初始裂缝高度设置了3 cm、4 cm、5 cm、6 cm、7 cm、8 cm等六种工况．试件制作完成后，将试样放置到试验台上进行拉伸试验，通过传感器可以实时监测拉伸过程中的力-位移曲线，如图10所示．从图中可以看出断裂前，随着位移的增大，拉伸应力基本呈线性增大，当试件断裂时拉伸应力发生骤降，这是由于试样为脆性破坏，拉断的瞬间应力降为0．因此，峰值荷载即为断裂荷载，根据式（7）可以计算出材料的断裂韧性．各工况测得的断裂韧性见表2．图11给出了拉断后的试样，可以看出试样基本平行于初始裂缝开裂，说明开裂模式符合张开型断裂．
为了验证断裂韧性计算公式修正后的准确性，将修正前式（4）计算结果与修正后进行了对比，如图12所示，从图中可以看出修正公式得出的断裂韧性约为42 kN/m3/2，且波动较小，而修正前公式计算得到的结果偏小，且随着初始裂缝增大，断裂韧性越来越小，说明边界效应越来越明显．这是由于式（4）是基于缝尖距离边界无限远得出的，当试件高度一定时，初始裂缝长度越大，缝尖距离边界越近，从而导致结果误差越大．当初始裂缝长度接近0时，可以认为缝尖距离边界无穷远，此时的结果可以认为是准确的．因此，对修正前的结果进行线性拟合，得到拟合公式如下
式中，KIC为断裂韧性，a为初始裂缝长度．当a=0 cm时，断裂韧性KIC为39.1 kN/m3/2，与修正公式的计算结果基本一致，从而验证了本公式的准确性．
因此，通过试验结果对修正后断裂韧性计算公式的验证，以及假设初始裂缝长度为0时的理论公式进一步验证，可以证明本试验方法及公式的准确性，从而可以用于腻子等低强度材料断裂韧性的测试．
4　结论
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本文对紧凑拉伸试验进行了改进，推导了张拉断裂韧性的计算公式，并基于边界效应的影响对公式进行了修正，之后采用多组紧凑拉伸试验，对修正公式的准确性进行了验证．主要结论如下
（1）对标准紧凑拉伸试验进行了改进，使其适用于低强度材料的拉伸断裂测试，并给出了试验原理及测试方法．
（2）基于断裂力学基本理论推导出了应力强度因子计算公式，并基于边界效应的影响对公式进行了修正，得到的修正公式可以直接计算出材料的断裂韧性．此外，应力强度因子与有限边界效应无关，与相对边界条件有关，且随着初始裂缝增大，边界效应越明显．
（3）试验结果表明试样的断裂形式符合张开型断裂，修正公式得出的断裂韧性约为42 kN/m3/2，且波动较小．试验验证了改进后试验方法及修正公式的准确性，从而可以用于腻子等低强度材料断裂韧性的测试．
基金
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  • 沧州市重点研发计划指导项目(213109013)
  • 河北水利电力学院基本科研业务(SYKY2101)
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2025年第46卷第3期
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doi: 10.15959/j.cnki.0254-0053.2025.03.020
  • 接收时间：2025-02-03
  • 首发时间：2026-03-24
  • 出版时间：2025-09-25
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  • 收稿日期：2025-02-03
基金
沧州市重点研发计划指导项目(213109013)
河北水利电力学院基本科研业务(SYKY2101)
作者信息
    1.河北水利电力学院　土木工程系，河北　沧州　061001
    2.河北省岩土工程安全与变形控制重点实验室（河北水利电力学院），河北　沧州　061001
    3.北京交通大学　土木建筑工程学院，北京　100010

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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
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
栓菌属 Trametes 5 2.39
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