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水灰比不同三点弯曲断裂韧度(波兰)

Effect of water/cement ratio and silica fume addition on the fracture toughness and morphology of fractured surfaces of gravel concretes

G.Prokopski a,*,https://www.sodocs.net/doc/5b14353723.html,ngier b

a Rzeszo?w University of Technology,Powstan?co?w Warszawy6,35-959Rzeszo?w,Poland

b Technical University of Cze?stochowa,Akademicka3,42-200Cze?stochowa,Poland

Received12November1999;accepted5June2000

Abstract

The results of the fracture toughness investigations for concretes made from natural gravel aggregate,with diverse water/cement ratio (W/C=0.33,0.43,0.53and0.63),without silica fume and with a silica fume addition are discussed.The critical values of the stress intensity factor,K Ic S,as well as,the critical values of crack tip opening displacement,CTOD c were determined.Also,the examination results for profile roughness parameter,R L,and fractal dimension,D,of concrete specimen fractures obtained in fracture toughness tests were performed.The largest values of the stress intensity factor,K Ic S,were showed by concretes with the lowest water/cement ratio,W/C=0.33 (both with and without silica fume addition).This was caused by considerably lower porosity of the aggregate±cement paste transition zone as observed in microstructural examinations,which had in this case a compact structure with a small number of structural defects.Cracks, upon reaching the critical force P Q,ran through the coarse aggregate grains,and the obtained fractures were flat in character.The examined parameters of fracture morphology,i.e.,the profile line development degree,R L,and the fractal dimension,D,reached the smallest values for those fractures.As the water/cement ratio increased,an increase in the structural porosity of the aggregate±cement paste transition zone occurred,which caused a promoted propagation of cracks and resulted in the obtaining of lower values of stress intensity factor,K Ic S. Cracks in this case propagated avoiding coarse gravel grains(an overgrain fracture formed),which resulted in increased fracture surface roughness and in a rise of the values of both examined parameters of fracture surface morphology,R L and D.D2000Elsevier Science Ltd. All rights reserved.

Keywords:Interfacial transition zone;Fracture toughness;Silica fume;Concrete

1.Introduction

Concrete is a multi-phase material,which makes its properties impossible to be determined without an analysis of the effect of its individual components on the service properties and designation for various applications.Being the most common material in building construction,con-crete is continuously subject to intensive and comprehen-sive investigations.

Of the factors that influence the properties of concrete, particular importance is attributed to the aggregate±cement paste transition layer that is regarded as the most sensitive area within the structure of concrete.The structure of the transition zone,and thus its properties,are influenced by several factors,such as the type of components used(coarse aggregate,cement,additions and admixtures)and the water±cement ratio.A particularly significant role is attrib-uted to the latter of the above factors,which has been confirmed by numerous studies in which an increased porosity has been found to occur in the area of the aggregate±cement paste interface caused by the higher water/cement ratio in this region with a simultaneous decrease in water/cement in the bulk of the matrix[1,2]. The examinations of the matrix structure clearly indi-cate the occurrence of porosity gradient with the maximum at the surface of the aggregate grains[3±5].The cause of the increased porosity and the related properties of the transition zone are ascribed by many researchers to water/ cement ratio.

According to Ref.[6],the structure of porosity of the transition zone,its thickness and properties,are all closely

*Corresponding author.Tel.:+48-17-865-1439;fax:+48-17-854-3365.

E-mail address:grzeprok@ewa.prz.rzeszow.pl(G.Prokopski).

Cement and Concrete Research30(2000)1427±1433

related to water/cement ratio.Ref.[7]reports that the local increase in water/cement in the area of the aggre-gate±cement paste interface is proportional to the amount of free unbound water,and any action increasing the contents of the solid phase reduces the effect of the transition zone on the strength properties of concrete. According to Ref.[8],water/cement has little effect on the transition zone thickness,while substantially influen-cing its porosity.

The increase in water/cement at the surface of aggregate grains is most commonly explained by the so-called``wall effect''caused by the difference in the grain size between aggregate and cement.

The evaluation of the effect of the transition zone on the strength properties of concretes has been increasingly per-formed in recent years.While applying for this purpose, studies utilising the methods of fracture mechanics that relate the obtained strength parameters to the structural defects(primary cracks)which,in the case of concretes, are unavoidable.It results from the microstructural studies (e.g.,Ref.[9])that it is the transition zone,and specifically, the aggregate±cement paste interface,where the greatest number of defects occur,and that the concrete failure process commences at the transition zone.

The morphology of the fracture surface occurring in the fracture process is a function of the material structure and,in the case of concrete,depends on the properties of the particular components and their sieving curves,the spatial configuration and interaction of phases,as well as on many interdependent mechanical and physical conditions of the failure process.

In order to determine the actual relationships between the structure and mechanical properties of concretes,it is necessary to use fractal geometry to describe the surface of fractures.This is caused by the strong irregularities of the fracture surfaces of concretes,which makes traditional Euclidean geometry unsuitable for this purpose.

The use of fractal analysis for describing the fracture surface of concretes is a relatively new research method(as compared to its use for,e.g.,metals).This method has proved very effective because of the strong inhomogeneity of concretes[10±15].

The development of fractal geometry was initiated by Mandelbrot[16,17],who worked out the theoretical bases for the description of irregular(self-similar)curves and introduced the concept of``fractal''(Lat.fractusDbroken, made up of fractions)to many branches of science. Fractal dimension is defined by the relationship corre-sponding to the segment of the line from which the fractal line is generated[Eq.(1)][16]:

ln N

ln 1a r

or N 1a r D 1

where N is the number of sub-parts for which the initial segment of unit length is divided at each step,r is the length of each sub-part,1/r is the scaling factor.

Fractal dimension D characterizes the irregularity of fractal objects.A straight line has a fractal dimension D=1,a curve has a fractal dimension D contained between the values1and2,depending on the degree of its devel-opment,whereas for surfaces fractal dimension lies in the range from2to3.The more irregular object,the greater is its fractal dimension D.

The generation of a fractal line may be repeated indefi-nitely and the total length of the line is expressed as a function of r and D by the following relationship[Eq.(2)]: L L o rà Dà1 2 where L is actual length of profile line and L o is the length of the initial straight segment.

The problem of the description of fracture morphol-ogy(in studies on steels)was dealt with,among others, Pickens and Gurland[18],who proposed profile rough-ness parameter,R L,as another measure of fracture roughness,defined as the relation of the actual fracture line length,L,to the length of its projection onto the reference line,L o[Eq.(3)]:

R L L a L o 3 The characterization of the fracture surface after the analysis of profiles is based on an assumption that having determined the profile roughness parameter,R L,it is possi-ble to define the fracture roughness parameter[Eq.(4)]: R S S a S o 4 where S is actual fracture area and S o is the apparent projected area,and projection is on the mean or average topographic plane.

A practical method of performing the examination of fractal fracture surfaces as obtained from fracture toughness tests,using a digitizer and an IBM PC computer is de-scribed,e.g.,in Ref.[14].

Despite the fact that the problem of the effect of the transition zone on the properties of concretes has been intensively investigated by numerous researchers,no single model has been developed so far,which would explain the cause for the formation of the transition zone;also,it has not been established how great the effect of this zone is on the properties of concretes.

2.Purpose and scope of the examinations

The paper presents the results of studies on the effects of the water/cement ratio and silica fume addition on the fracture toughness of gravel concrete.Fracture toughness tests were performed using Mode I(tension at bending) according to the RILEM Draft Recommendations[19].The critical values of stress intensity factors,K Ic S,and critical crack tip opening displacement,CTOD c,were determined. The concrete mixtures were prepared from Portland cement with``35''grade additions supplied by Rudniki

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Cement Plant at Cze ?stochowa (Poland),0?2mm sand,gravel with a grain size of up to 16mm,and superplasti-cizer.Four batches of concrete mixtures were prepared with the following water /cement ratios:series GA DW /C =0.33;series GB DW/C =0.43;series GC DW/C =0.53;series GD DW/C =0.63.The concrete mixture of the basic series GB (W/C =0.43)was designed as an experimental method as a plastic mixture.

Also,four series of concrete mixtures were made with an addition of 10%silica fume (series GMA,GMB,GMC,and GMD),with the same water/cement ratios as those in the previous mixtures.The silica fume constituted 10%of the cement mass,and was a replacement for fine aggregate,i.e.,it reduced the sand mass by 10%.In those mixtures,the sand point of the aggregate mixture was maintained constant at 30%.

A superplasticizer was added to the GA and GMA series mixture.The compositions of the concrete mixtures and the results of the compressive strength tests are summarised in Table 1.

From each concrete mixture,five 0.15m sample cubes were prepared for compressive tests,and six 0.7?0.15?0.08m beams with a single initial crack for testing according to Mode I of fracture (according to Ref.[19]).The initial cracks were made by the insert-moulding of 3mm-thick steel blades with an apex angle of approximately 25°.The specimens were unmoulded after 24(cubes)and 48h (beams),and then cured in laboratory conditions until reach-ing the age of 28days.3.Fracture toughness tests

Tests according to Mode I of fracture were carried out using test specimen with dimensions as given in the RILEM

Draft Recommendations [19]:W =150mm,b =80mm,L =700mm,S =600mm,a o =50mm (Fig.1).

An MTS 810hydraulic testing machine was used in the tests.Loading rate was selected so that the maximum load was reached in approximately 5min.The applied load was reduced at approximately 95%post-peak load.After reducing the load to zero,the test specimen was loaded again.For each test specimen,six to eight loading±unloading cycles were completed,while recording plots of the loading force as a function of crack mouth opening displacement (CMOD).An example plot of CMOD vs.load increment is shown in Fig.2.Based on the plots obtained for each test specimen,the following quantities were determined:Young's modulus,E ;critical effective crack length,a c ;critical stress intensity factor,K Ic S ,and critical CTOD c .

Table 1

Compositions of the concrete mixtures and their average compressive strengths Concrete type GA GB GC GD W /C

0.430.530.630.33

Mixture composition,[kg]:Cement 357

357357357Aggregate 1911191119111911Water 155191226119

Plasticizer

±±± 3.3%of cement mass Compressive strength,R ?c [MPa]56.047.232.463.8Concrete type GMA GMB GMC GMD W /C

0.430.530.630.33

Mixture composition,[kg]:

Cement 357357357357Aggregate 1876187618761876Water

155191226119Silica fume 35353535

Plasticizer

±±± 3.3%of cement mass Compressive strength,R

?c [MPa]62.5

51.1

40.2

73.7

Fig.1.Schematic drawings of the specimen used in the fracture toughness examination according to Mode I,HO Dclamp gauge holder thickness,CMOD Dcrack mouth opening displacement.

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The critical stress intensity factor K Ic S was calculated from the following relationship [Eq.(5)][19]:

K S

3 P max 0X 5w S a c 1a 2F a 2W 2b Y 5 in which:

F a

1X 99àa 1àa 2X 15à3X 93a 2X 7a 2

1a 2 1 2a 1àa 3a 2

q Y where P max =maximum load,a =a c /W ,w =w o S /L ,w o =spe-cimen weight [N],S ,a o ,W ,b ,L Daccording to Fig.1.CTOD c was determined from the relationship below [Eq.(6)][19]:CTOD c

6P max Sa c V 1 a

EW 2b

? 1àb 2 1X 081à1X 149a ? b àb 2 1a 2Y

where b =a o /a (a =a o before loading).The results of the tests according to Mode I of fracture are shown in Table 2.

From the obtained test results,relationships of stress intensity factor K Ic S vs.water/cement ratio,W/C,were determined.Figs.3and 4show suitable graphs of regres-sion equations (solid lines),confidence intervals for the

regression equations,and confidence intervals for any predictable value of dependent variable as calculated from the regression equations (dotted lines),as well as the average values of the specimen testing results for assumed water/cement ratios.

The performed studies have shown a good sensitivity of stress intensity factor K Ic S to the changes in the aggregate±cement paste transition layer,caused by the change in the water contents of the concrete mixture and addition of silica fume.A clear relationship has been found to exist between water/cement ratio,W/C,and the stress intensity factor K Ic S tested.Increased amount of water in the concrete mixtures caused a significant drop in K Ic S :

In concretes without silica fume from the value of 3.26MNm à3/2at W/C=0.33down to 1.80MNm à3/2at W/C=0.63(Fig.3);

In concretes with silica fume from the value of 3.57MNm à3/2at W/C=0.33down to 2.07MNm à3/2at W/C=0.63(Fig.4).

In Figs.3and 4,regression equation graphs (solid lines),regression equation confidence intervals (dotted lines),

and

Fig.2.An example graph of CMOD ±load relationship obtained in the tests.

Table 2

Average values of fracture mechanics parameters obtained in the tests Concrete type Series GA Series GB Series GC Series GD K Ic S

[MNm à3/2

] s

2.72 0.20 2.28 0.14 1.80 0.09

3.26 0.24CTOD c s á[103

cm] 3.25 0.19 3.71 0.19 2.97 0.22 3.60 0.1Concrete type Series GMA Series GMB Series GMC Series GMD K Ic S [MNm à3/2] s 2.91 0.25 2.44 0.12 2.07 0.07 3.57 0.16CTOD c s á[103cm]

3.77 0.43

3.57 0.21

3.41 0.33

3.73

0.19

Fig.3.Relationship of K Ic S vs.W /C (concretes without silica fume).

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confidence intervals for an arbitrary expected value of dependent variable as calculated from the regression equa-tions (broken lines)are shown.

The tests for CTOD c did not reveal a positive relationship between this parameter and the changes in the structure of the aggregate±cement paste transition layer.4.Fracture morphology examination

The quantitative description of fracture morphology was done based on the analysis of the specimen fracture profile lines obtained in the fracture toughness tests.Subjected to tests were three fractures selected randomly from each series of concretes.White gypsum paste was poured over the obtained fracture surfaces.After the paste had set,a gypsum replica was taken from the concrete fracture,onto which colored gypsum paste was then poured.The replicas were mechanically cut vertically to the mapped fracture surface.The images of replica layers were input to a computer in the form of bitmaps using a scanner.Then,the printout of particular layers was done at a five-time magnification,which enabled the precise mapping of profile lines.Data for

the coordinates of profile line generating points were entered to the computer using a digitizer.The digitization process was accomplished using the ``operator's point selection''method [20].

Fractal dimension,D ,and the actual length of profile lines,R L ,were calculated using the FRACTAL 8software developed at the Materials Engineering Department of the Technical University of Cze ?stochowa (Poland).The ob-tained examination results are presented in Table 3.Based on the obtained examination results,the relationships of fractal dimensions,D ,and the profile roughness parameter,R L ,have been established as a function of stress intensity factors,K Ic S (Figs.5and 6).The dependence of

profile

Fig.4.Relationship of K Ic S vs.W /C (concretes with silica fume).Table 3

Values of profile roughness parameter,R L ,and fractal dimension,D Concrete type K Ic S [MNm à3/2]R L D GA 2.72 1.088 1.022GB 2.28 1.109 1.028GC 1.80 1.140 1.031GD 3.26 1.067 1.014GMA 2.91 1.072 1.018GMB 2.44 1.093 1.022GMC 2.07 1.108 1.025GMD

3.57

1.059

1.012

Fig.5.Dependence of fractal dimension,D ,on K Ic S

Fig.6.Dependence of profile roughness parameter,R L ,on K Ic S .

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roughness parameter,R L ,on fractal dimension,D ,has also been determined (Fig.7).

In Fig.5,6and 7,regression equation graphs (solid lines),regression equation confidence intervals (dotted lines),and confidence intervals for an arbitrary expected value of dependent variable as calculated from the regres-sion equations (broken lines)are shown.

The analysis of fracture surface morphology carried out by utilizing the profile line development degree,R L ,and the fractal dimension,D ,has shown a close relationship exists between these parameters and the stress intensity factor,K Ic S .Larger values of the stress intensity factor,K Ic S corresponded to lower values of both R L and D .

In the case of concrete with no silica fume addition,the profile line development degree,R L ,decreased from the value of 1.14at W/C=0.63(K Ic S =1.80MNm à3/2)to the value of 1.067at W/C=0.33(K Ic S =3.26MNm à3/2).The fractal dimension D decreased from the value of 1.031at W/C =0.63to the value 1.014at W/C=0.33.

For concretes with a silica fume addition,the same trends in the change of both examined parameters were observed.The profile line development degree R L decreased from the value of 1.093at W/C=0.63(K Ic S =2.07MNm à3/2)to the value of 1.059at W/C=0.33(K Ic S =3.57MNm à3/2).The fractal dimension D decreased from the value 1.025at W/C=0.63to the value of 1.012at W/C=0.33.5.Conclusions

The studies on the effect of water contents in concrete mixtures and the addition of silica fume using stress intensity factor K Ic S and morphological examinations are

an effective means for the evaluation of the effect of structure changes on the fracture toughness of concretes.A clear relationship has been found to exist between water/cement ratio (W/C)and the stress intensity factor K Ic S tested.Increased amount of water in the concrete mixtures caused a significant drop in K Ic S :

In concretes without silica fume from the value of 3.26MNm à3/2at W/C=0.33down to 1.80MNm à3/2at W/C=0.63;

In concretes with silica fume from the value of 3.57MNm à3/2at W/C=0.33down to 2.07MNm à3/2at W/C=0.63.

Addition of silica fume to the concrete mixtures resulted in the enhanced properties of the hardened concrete.Stress intensity factor K Ic S increased,respectively:for series GMA (W/C=0.33)Dby 15%,for series GMB (W/C=0.43)Dby 7%,for series GMC (W/C=0.53)Dby 9.5%,and for series GMD (W/C=0.63)Dby 24%.

The tests for the critical crack tip opening displacement CTOD c did not reveal a positive relationship between this parameter and the changes in the structure of the aggregate±cement paste transition layer.

Changes in the stress intensity factor K Ic S are closely related to the changes in the structure of the concretes as observed in the morphological examinations.

Examinations of the fracture surface morphology have shown that the profile roughness parameter,R L ,and fractal dimension,D ,of the fracture occurring in the fracture process are closely dependent on the fracture toughness of concrete.

It was found that with increasing stress intensity factor,K Ic S ,profile roughness parameter,R L ,and fractal dimension,D ,for both concretes (without and with silica fume)decreased.

The drop in the line development degree R L and the fractal dimension D with increasing fracture toughness (K Ic S )of concretes was caused by the increased strength of the aggregate±cement paste transition zone and by larger forces of adhesion of the cement paste to the gravel grains,due to the reduced porosity of this zone (lower both water/cement and the silica fume addition).

In the case of the GA series concrete of (W/C=0.33)and the GMA series concrete (W/C=0.33with silica fume added),the forces of adhesion of the aggregate to the cement paste were high (higher than the strength of gravel grains),which resulted in the propagation of cracks through the coarse aggregate grains and the formation of flat-surface fractures;the values of R L and D obtained in the tests were the smallest.

In the case of concretes with a large water/cement ratio (the GD and GMD series),the aggregate±cement paste transition zone was highly porous and weak,which resulted in the development of a crack in this zone;the so-called overgrain fractures,highly irregular and rough,for

which

Fig.7.Dependence of profile roughness parameter,R L ,on fractal dimension D .

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both the profile line development degree R L and the fractal dimension D had relatively large values.

The obtained relationships of profile roughness para-meter,R L,and fractal dimension D,as a function of stress intensity factor,K Ic S,as well as the dependence R L=f(D) show,for a particular concrete,a high level of correlation, which indicates a high susceptibility of the examined fracture morphology parameters,R L and D,to changes in the structure of concretes and obtained critical values of stress intensity factor,K Ic S.

The microstructural examinations(see Ref.[21])showed that the aggregate±cement paste transition zone in concrete from gravel aggregate with a small water/cement ratio (concrete without silica fume addition)and both with a small water/cement ratio and a silica fume addition was uniform and dense,with only a small number of structural discontinuities.A transgranular character of fracture was observed in this case,that its cracks going through the aggregate grains,which caused the formation of a flat fracture surface.The strength of the aggregate±cement paste interface was in this case higher than the strength of gravel grains,which resulted in the critical values of stress intensity factors,K Ic S,having the greatest values for this series of concrete.

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金属材料-准静态断裂韧性测试的方法

ICS 77.040.10 Ref. No. ISO 12135:2002/Cor.1:2008(E) ? ISO 2008 – All rights reserved Published in Switzerland INTERNATIONAL STANDARD ISO 12135:2002 TECHNICAL CORRIGENDUM 1 Published 2008-06-01 INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ? МЕЖДУНАРОДНАЯ ОРГАНИЗАЦИЯ ПО СТАНДАРТИЗАЦИИ ? ORGANISATION INTERNATIONALE DE NORMALISATION Metallic materials — Unified method of test for the determination of quasistatic fracture toughness TECHNICAL CORRIGENDUM 1 Matériaux métalliques — Méthode unifiée d'essai pour la détermination de la ténacité quasi statique RECTIFICATIF TECHNIQUE 1 Technical Corrigendum 1 to ISO 12135:2002 was prepared by Technical Committee ISO/TC 164, Mechanical testing of metals , Subcommittee SC 4, Toughness testing — Fracture (F), Pendulum (P), Tear (T). Page 1, Clause 2 Replace the reference to ISO 7500-1:— with the following: ISO 7500-1, Metallic materials — Verification of static uniaxial testing machines — Part 1: Tension/compression testing machines — Verification and calibration of the force-measuring system Delete the reference to Footnote 1) and the footnote “To be published. (Revision of ISO 7500-1:1999)”. Page 13, Figure 6 Add “(not to scale)”. Move the note from under the title of Figure 6 to above the title. Page 16, Figure 9, Footnote d) Replace “on” with “or” to give d Edge of bend or straight compact specimen.

断裂韧性实验报告

断裂韧性测试实验报告随着断裂力学的发展，相继提出了材料的IC K 、()阻力曲线J J R 、)(阻力曲线CTOD R δ等一些新的力学性能指标，弥补了常规试验方法的不足，为工程应用提供了可靠的断裂判据和设计依据。下面介绍下这几种方法的测试原理及试验方法。 1、三种断裂韧性参数的测试方法简介 1. 1 平面应变断裂韧度IC K 的测试对于线弹性或小范围的I 型裂纹试样，裂纹尖端附近的应力应变状态完全由应力强度因子I K 所决定。I K 是外载荷P ，裂纹长度a 及试样几何形状的函数。在平面应变状态下，当P 和a 的某一组合使I K =IC K ，裂纹开始失稳扩展。I K 的临界值IC K 是一材料常数，称为平面应变断裂韧度。测试IC K 保持裂纹长度a 为定值，而令载荷逐渐增加使裂纹达到临界状态，将此时的C P 、a 代入所用试样的I K 表达式即可求得IC K 。 IC K 的试验步骤一般包括：（1）试样的选择和准备（包括试样类型选择、试样尺寸确定、试样方位选择、试样加工及疲劳预制裂纹等）；（2）断裂试验；（3）试验结果的处理（包括裂纹长度a 的测量、条件临界荷载Q P 的确定、实验测试值Q K 的计算及Q K 有效性的判断）。

1. 2 延性断裂韧度R J 的测试 J 积分延性断裂韧度是弹塑性裂纹试样受I 型载荷时，裂纹端点附近区域应力应变场强度力学参量J 积分的某些特征值。测试J 积分的根据是J 积分与形变功之间的关系： a B U J ??-= （1-1）其中U 为外界对试样所作形变功，包括弹性功和塑性功两部分，a 为裂纹长度，B 为试样厚度。 J 积分测试有单试样法和多试验法之分，其中多试样法又分为柔度标定法和阻力曲线法。但无论是单试样法还是多试样柔度标定法，都须先确定启裂点，而困难正在于此。因此，我国GB2038-80标准中规定采用绘制R J 阻力曲线来确定金属材料的延性断裂韧度。这是一种多试样法，其优点是无须判定启裂点，且能达到较高的试验精度。这种方法能同时得到几个J 积分值，满足工程实际的不同需要。所谓R J 阻力曲线，是指相应于某一裂纹真实扩展量的J 积分值与该真实裂纹扩展量的关系曲线。标准规定测定一条R J 阻力曲线至少需要5个有效试验点，故一般要58件试样。把按规定加工并预制裂纹的试样加载，记录?-P 曲线，并适当掌握停机点以使各试样产生不同的裂纹扩展量（但最大扩展量不超过0.5mm ）。测试各试样裂纹扩展量a ?，计算相应的J 积分，对试验数据作回归处理得到R J 曲线。R J 阻力曲线的位置高低和斜率大小代表了材料对于启裂和亚临界扩展的抗力强弱。 R J 阻力曲线法测试步骤一般包括：（1）试样准备

材料的韧性及断裂力学简介

第二节材料的韧性及断裂力学简介一、低应力脆断及材料的韧性人们在对船舶的脆断、无缝输气钢管的脆断裂缝、铁桥的脆断倒塌、飞机因脆断而失事、石油、电站设备因脆断而发生重大事故的分析中，发现了一些它们的共同特点： 1.通常发生脆断时的宏观应力很低，按强度设计是安全的； 2.脆断事故通常发生在比较低的工作温度环境下； 3.脆断从应力集中处开始，裂纹源通常在结构或材料的缺陷处，如缺口、裂纹、夹杂等； 4.厚截面、高应变速率促进脆断。由此，人们发现了传统设计思想和材料的性能指标在强度设计上的不足，试图提出新的性能指标和安全判据，找到防止脆断的新的设计方法。传统的强度设计所依据的性能指标主要为弹性模量E、屈服极限σs、抗拉强度σb，而塑性指标延伸率δ和面收缩率φ在设计中只是参考数据，通常还会考虑应力集中现象，即使如此，设计的安全判据仍不足以防止脆断的发生，这说明材料的强度、塑性、弹性这些性能指标还不能完全反映材料抵抗脆断的发生。经过对众多脆断事故的分析和研究，人们提出了一个便于反映材料抗脆断能力的新的性能指标——韧性，从使脆性材料和韧性材料断裂所消耗的能量不同，归纳出韧性的定义为：所谓韧性是材料从变形到断裂过程中吸收能量的太小，它是材料强度和塑性的综合反映。例如图l-2为球墨铸铁和低碳钢的拉伸曲线，可以用拉伸曲线下的面积来表示材料的韧性，即图中可见，虽然球墨铸铁的抗拉强度σb比低碳钢高，但其断裂时的塑性应变εp确远较低碳钢小，综合起来看，低碳钢的韧性高。图1-2 球铁和低碳钢拉伸曲线表示的韧性材料的韧性可用实验的方法测试和判定。应用较早和较广泛的是缺口冲击试验，这种方法已经规范化。具体方法是将图1-3所示的缺口试样用专用冲击试验机施加冲击载荷，使试样断裂，用冲击过程中吸收的功除以断口面积，所得即为材料的冲击韧性，以αk表示，单位为J/cm^2。目前国际上多用夏氏V型缺口试样，我国多用U型缺口试样。由于缺口冲击

断裂韧性KIC的测定

材料力学性能实验报告姓名：刘玲班级：材料91 学号：09021004 成绩：的测定实验名称断裂韧性K IC 实验目的了解金属材料平面应变断裂韧性测试的一般原理和方法实验设备 1.万能材料试验机一台（型号CSS-88100) 2.位移传感器及自动记录装置 3.游标卡尺一把 4.显微测试仪一台 5.三点弯曲试样四个试样示意图

试样宏观断口示意图（韧断，脆断）图1 20钢脆断图2 40铬韧性断口

实验记录及Q P 的确定表1 裂纹长度a 1a /mm 2a /mm 3a /mm 4a /mm 5a /mm a /mm 03 2.478 5.0085 5.5680 5.2430 3.1925 5.2432 09 2.757 3.9505 4.134 3.992 3.1790 4.0255 403 2.800 3.4065 3.7085 3.4915 2.9185 3.5355 407 1.986 2.6595 2.9970 2.5970 16810 2.7512 表2 试样各数据试样编号试样材料屈服强度(MPa) 高度W(mm) 宽度B(mm) 03 40Cr800℃+ 100℃回火 1050 25.00 12.50 09 25.00 12.50 403 20#钢退火态 370 25.00 12.00 407 25.00 12.00 表3 各试样实验测得的Q P 值及max P 试样编号 Q P (N) max P (N) 03 13270.126 13270.126 09 26650.307 26650.307 403 407 14523.800 16479.500

几种土体断裂韧度的测试方法

几种土体断裂韧度的测试方法摘要：断裂韧度的测试是断裂力学研究的重要部分，根据对裂缝加载方式不同，断裂韧度可分为Ⅰ型加载下的断裂韧度、Ⅱ型加载下的断裂韧度、Ⅲ型加载下的断裂韧度三种基本形式。目前对金属、岩体等材料的断裂韧度测试方法已有了大量的研究，形成了相应的测试规范。土体断裂破坏主要是Ⅰ型断裂破坏和Ⅱ型断裂，但土体由于其自身材料性质的特殊性，并不能完全采用其他材料的测试规范。结合土体材料的特性介绍了土体Ⅰ型断裂和Ⅱ型断裂的断裂韧度的几种常用测试方法，并对几种方法的优缺点和适用性进行了讨论。关键词：土体，断裂力学，断裂韧度，试验方法引言断裂力学是用来研究含有宏观裂纹型缺陷的材料或构件, 在外力作用下裂纹扩展的规律。从狭义角度解释, 它可用来研究含有宏观裂纹型缺陷的材料或构件, 在外力作用下裂纹扩展的规律。当土体内存在宏观贯通裂纹时, 在外荷载作用下裂纹尖端前缘将产生应力集中。在应力集中区域内的应力值, 远比由外荷载所引起的平均应力值大。传统的材料力学设计方法不能用来判断裂纹是否失稳扩展, 而应根据以研究断裂韧性参数和能量释放率为基础的断裂力学方法来进行判断。对于各种复杂的断裂形式，总可以分解成为三种基本断裂类型的组合。这三种基本断裂类型即为Ⅰ型断裂、Ⅱ型断裂、Ⅲ型断裂。Ⅰ型断裂属于张开型断裂，Ⅱ型断裂属于滑移型断裂，Ⅲ型断裂断裂属于撕裂型断裂[1]。由于土的抗拉强度很低, 因此判别土体是否会出现张开型裂纹失稳扩展, 就成为工程技术人员首先关心的问题。目前国内外虽有一些研究人员开始从事岩石、混凝土等材料的断裂韧度研究, 但对于土体的断裂韧度研究至今较少进行。现将土体的断裂韧度测试方法综述如下。 1 土体应力强度因子及断裂韧度当进行Ⅰ型加载，即发生Ⅰ型断裂时，其裂纹端部区域的应力分量可以应用弹性理论解得：

断裂韧性实验报告

断裂韧性测试实验报告随着断裂力学得发展,相继提出了材料得、、等一些新得力学性能指标,弥补了常规试验方法得不足,为工程应用提供了可靠得断裂判据与设计依据。下面介绍下这几种方法得测试原理及试验方法。 1、三种断裂韧性参数得测试方法简介 1、１平面应变断裂韧度得测试对于线弹性或小范围得型裂纹试样,裂纹尖端附近得应力应变状态完全由应力强度因子所决定。就是外载荷,裂纹长度及试样几何形状得函数。在平面应变状态下,当与得某一组合使=，裂纹开始失稳扩展。得临界值就是一材料常数,称为平面应变断裂韧度。测试保持裂纹长度a为定值,而令载荷逐渐增加使裂纹达到临界状态，将此时得、代入所用试样得表达式即可求得。得试验步骤一般包括：（1）试样得选择与准备(包括试样类型选择、试样尺寸确定、试样方位选择、试样加工及疲劳预制裂纹等); （2）断裂试验; （3）试验结果得处理(包括裂纹长度得测量、条件临界荷载得确定、实验测试值得计算及有效性得判断）。 1、２延性断裂韧度得测试积分延性断裂韧度就是弹塑性裂纹试样受型载荷时,裂纹端点附近区域应力应变场强度力学参量积分得某些特征值。测试积分得根据就是积分与形变功之间得关系: (1－1）其中为外界对试样所作形变功,包括弹性功与塑性功两部分,为裂纹长度,为试样厚度。

积分测试有单试样法与多试验法之分,其中多试样法又分为柔度标定法与阻力曲线法。但无论就是单试样法还就是多试样柔度标定法,都须先确定启裂点,而困难正在于此。因此,我国GB２０38-８０标准中规定采用绘制阻力曲线来确定金属材料得延性断裂韧度。这就是一种多试样法,其优点就是无须判定启裂点，且能达到较高得试验精度。这种方法能同时得到几个积分值,满足工程实际得不同需要。所谓阻力曲线，就是指相应于某一裂纹真实扩展量得积分值与该真实裂纹扩展量得关系曲线。标准规定测定一条阻力曲线至少需要5个有效试验点,故一般要5 8件试样。把按规定加工并预制裂纹得试样加载，记录曲线，并适当掌握停机点以使各试样产生不同得裂纹扩展量(但最大扩展量不超过0、５mｍ)。测试各试样裂纹扩展量,计算相应得积分，对试验数据作回归处理得到曲线。阻力曲线得位置高低与斜率大小代表了材料对于启裂与亚临界扩展得抗力强弱。阻力曲线法测试步骤一般包括：（1）试样准备 ①试样尺寸得选择原则： 1)平面应变条件：标准规定 (1-２）其中 2)积分有效性条件一般，当不易估计时,可用求出得估计值 ②疲劳预制裂纹:

(完整版)断裂力学试题

2007断裂力学考试试题 B 卷答案一、简答题（本大题共5小题，每小题6分，总计30分） 1、（1）数学分析法:复变函数法、积分变换；（2）近似计算法：边界配置法、有限元法；（3）实验标定法：柔度标定法；（4）实验应力分析法：光弹性法. 2、假定：（1）裂纹初始扩展沿着周向正应力θσ为最大的方向；（2）当这个方向上的周向正应力的最大值max ()θσ达到临界时,裂纹开始扩展. 3、应变能密度:r S W = ，其中S 为应变能密度因子，表示裂纹尖端附近应力场密度切的强弱程度。 4、当应力强度因子幅值小于某值时，裂纹不扩展，该值称为门槛值。 5、表观启裂韧度，条件启裂韧度，启裂韧度。二、推导题（本大题10分） D-B 模型为弹性化模型，带状塑性区为广大弹性区所包围，满足积分守恒的诸条件。积分路径：塑性区边界。 AB 上：平行于1x ，有s T dx ds dx σ===212,,0 BD 上：平行于1x ，有s T dx ds dx σ-===212,,0 5分 δ σσσσΓ s D A s D B s B A s BD A B i i v v v v dx x u T dx x u T ds x u T Wdx J =+=+-=??-??-=??-=???)()(1 122112212 5分三、计算题（本大题共3小题，每小题20分，总计60分） 1、利用叠加原理:微段→集中力qdx →dK = Ⅰ ?0 a K =?Ⅰ 10分 A

令cos cos x a a θθ==,cos dx a d θθ= ?111sin () 10 cos 22(cos a a a a a K d a θθθ--==Ⅰ 当整个表面受均布载荷时,1a a →. ?12()a a K -==Ⅰ 10分 2、边界条件是周期的: a. ,y x z σσσ→∞==. b.在所有裂纹内部应力为零.0,,22y a x a a b x a b =-<<-±<<±在区间内 0,0y xy στ== c.所有裂纹前端y σσ> 单个裂纹时 Z = 又Z 应为2b 的周期函数 ?sin z Z πσ= 10分采用新坐标:z a ξ=- ?sin ()a Z π σξ+= 当0ξ→时,sin ,cos 1222b b b π π π ξξξ== ?sin ()sin cos cos sin 22222a a a b b b b b π π π π π ξξξ+=+ cos sin 222a a b b b π π π ξ= + 222 2[sin ()]( )cos 2 cos sin (sin )2222222a a a a a b b b b b b b π π π π π π π ξξξ+=++

断裂韧性试验

断裂韧性试验创建时间：2008-08-02 test for fracture toughness 在线弹性断裂力学及弹塑性断裂力学基础上发展起来的一种评定材料韧性的力学试验方法（见断裂力学）。 20世纪以来，曾发生过多起容器、桥梁、舰船、飞机等脆断事故；事故分析查明，断裂大多起源于小裂纹。为解决金属脆断问题，美国在1958年组成ASTM断裂试验专门委员会，目的是建立有关测定材料断裂特性的试验方法。于1967年首次制定了用带疲劳裂纹的三点弯曲试样（图1 [两种常用断裂韧性试样]）测定高强度金属材料平面应变断裂韧性操作规程草案，并于1970年颁发了世界第一个断裂韧性试验标准ASTME399-70T。此后，断裂韧性试验受到世界各国的普遍重视并蓬勃发展。中国于1968年前后开始这方面的试验研究。取样原则由于裂纹或类裂纹缺陷是导致工程结构断裂的主要原因，所以断裂韧性试验采用带尖锐裂纹的试样(图1[两种常用断

裂韧性试样]),用直接观察或间接测量法连续监测裂纹的行为；如用夹式引伸计连续测量裂纹嘴张开位移随载荷的变化(图2[用夹式引伸计测裂纹嘴张开位移随载荷变化的曲线]随载荷变化的曲线" class=image>),以测定材料抗裂纹扩展的能力及裂纹在疲劳载荷或应力腐蚀下的扩展速率;求得平面应变断裂韧度[ic]、动态断裂韧度[id]、裂纹临界张开位移，应力腐蚀临界强度因子[111-21] [kg2],疲劳裂纹扩展速率d/d（毫米/周）等断裂韧性参数。其中，角标Ⅰ代表张开型裂纹，或称Ⅰ型裂纹,角标c代表临界值。此外，尚有滑开型（Ⅱ型）裂纹，撕开型（Ⅲ型）裂纹（图3 [裂纹的扩展类型示意图]）。Ⅰ型裂纹最易引起脆断，所以目前断裂韧性试验多限于Ⅰ型加载。

(完整版)断裂韧性KIC测试试验.docx

实验五断裂韧性K IC测试试验一、试样的材料、热处理工艺及该种钢材的σy 和KⅠC 的参考值本实验采用标准三点弯曲试样（代号SE（B）），材料为 40Cr，其热处理工艺如下： ①热处理工艺：860℃保温 1h，油淬； 220℃回火，保温0.5~1h ； ②缺口加疲劳裂纹总长：9~11mm （疲劳裂纹2~3.5mm） ③不导角，保留尖角。样品实测 HRC50，从机械手册中关于40Cr 的热处理实验数据曲线上查得： σy=σ0.2=1650MPa，σb=1850MPa，δ5=9%，ψ=34%，KⅠ C=42MN·m-3/2。二、试样的形状及尺寸国家标准 GB/T 4161-1984《金属材料平面应变断裂韧度KⅠC试验方法》中规定了两种测试断裂韧性的标准试样：标准三点弯曲试样（代号SE（ B））和紧凑拉伸试样（代号C(T)）。这两种试样的裂纹扩展方式都是Ⅰ型的。本实验采用标准三点弯曲试样（代号SE（ B））。试样的形状及各尺寸之间的关系如图所示：为了达到平面应变条件，试样厚度 B 必须满足下式： B≧ 2.5(KⅠC/ σ y)2 a≧ 2.5(KⅠC/ σ y)2 （W-a）≧ 2.5(KⅠC/ σ y)2 式中：σ y 0.2或 σ s 。 —屈服强度σ 因此，在确定试样尺寸时，要预先估计所测材料的KⅠC和σy值，再根据上式确定试样的最小厚度 B。若材料的KⅠC值无法估计，则可根据σy B 的大小，然后再确 /E 的值来确定定试样的其他尺寸。试样可从机件实物上切去，或锻、铸试样毛坯。在轧制钢材取样时，应注明裂纹面取向和裂纹扩展方向。试样毛坯粗加工后，进行热处理和磨削，随后开缺口和预制裂纹。试样上的缺口一般在钼丝电切割机床上进行切割。为了使引发的裂纹平直，缺口应尽可能地尖锐。开好缺口的试样，在高频疲劳试验机上预制裂纹。疲劳裂纹长度应不小于 2.5%W，且不小于 1.5mm 。 a/W 值应控制在 0.45~0.55 范围内。本试样采用标准三点弯曲试样（代号 SE（B）），其尺寸：宽 W=19.92mm ，厚 B=10.20mm 总长 100.03mm 。三、实验装置制备好的试样，在MTS810 材料力学试验机上进行断裂试验。对于三点弯曲试样，其试验装置如图5-2 所示。可将采集的试验数据以文件形式（数据采集间隔0.1s）存储在计算机中，同时利用3086-11 型 X— Y 系列实验记录仪绘制P— V 曲线。本实验跨距S 为 80mm ，弯曲压头速率0.01mm/s 。用 15J 型工具显微镜测量试样的临界裂纹(半 )长度 a。

陶瓷材料断裂韧性的测定

实验陶瓷材料断裂韧性的测定一、前言脆性材料的破坏往往是破坏性的，即材料中裂纹一旦扩展到一定程度，就会立即达到失稳态，之后裂纹迅速扩展。材料的断裂韧性可以用来衡量它抵抗裂纹扩展的能力，亦即抵抗脆性破坏的能力。它是材料塑性优劣的一种体现，是材料的固有属性。裂纹扩展有三种形式：掰开型(I型)、错开型(II型)、撕开型(III型)，其中掰开型是最为苛刻的一种形式，所以通常采用这种方式来测量材料的断裂韧性，此时的测量值称作K IC。在平面应变状态下材料K IC 值不受裂纹和几何形状的影响。因此，K IC值对了解陶瓷这一多裂纹材料的本质属性，具有非常重要的意义。目前，断裂韧性的测试方法多种多样，如：单边切口梁法(SENB)、双扭法（DT)、山形切口劈裂法、压痕法、压痕断裂法等。其中，有些方法技术难度较高，不太容易实现大规模实用化；有些方法会出现较大测量误差，应用起来存在一定困难。相对而言，比较普遍采用的SENB法，该方法试样加工较简单，裂纹的引入也较容易。本实验采用SENB法进行。但是，这种方法存在裂纹尖端钝化、预制裂纹宽度不易做得很窄等缺陷；另外，它适用于粗晶陶瓷材料，对细晶陶瓷其所测的K IC值偏大。二、仪器测试断裂韧性所需仪器如下： 1.材料实验机对测试材料施加载荷，应保证一定的位移加载速度，国标规定断裂韧性测试加载速度为0.05mm/min。 2.内圆切割机用于试样预制裂纹，金刚石锯片厚度不应超过0.20mm。 3.载荷输出记录仪输出并记录材料破坏时的最大载荷，负荷示值相对误差不大于1。本实验在材料实验机上配置了量程为980N的称重传感器输出载荷，采用电子记录仪记录断裂载荷。 4.夹具保证在规定的几何位置上对试样施加载荷，试样支座和压头在测试过程中不发生塑性变形，材料的弹性模量不低于200GPa。支座和压头应有与试样尺寸相配合的曲率半径，长度应大于试样的宽度，与试样接触部分的表面粗糙度R a（根据规定不大于1.6μm）。试样支座为两根二硅化钼发热体的小圆柱，置于底座两个凹槽上。压头固定在材料实验机的横梁上。 5.量具测量试样的几何尺寸和预制裂纹深度，精度为0.0lmm，需使用游标卡尺和读数显微镜。三、试样的要求试样的形状是截面为矩形的长条，试样表面要经过磨平、抛光处理，对横截面垂直度有一定的要求，边棱应作倒角。在试样中部垂直引入裂纹，深度大约为试样高度的一半，宽度应小于0.2mm。试样尺寸比例为： c/W=0.4～0.6 L/W=4 B≈W/2 式中：c－裂纹深度； W－试样高度；

(完整版)平面应变断裂韧度K1C的测定实验预案

平面应变断裂韧度K1C 的测定实验预案姓名：江维学号：M050110110 指导老师：钱士强学院：材料工程学院

、试样制备 1. 材料：先用40刚 2. (1) 厚度: 为确定试件尺寸，要根据试件各预先测定材料的0.2和K lC的估计值，根据上式确定试件的最小厚度，在尺寸之间的关系确定试件的其它尺寸。K lC的估计值可以借用相近材料的K IC值，也可根据材料的0.2/ E的值确定试件的尺寸，如下表所示：表

K C 2一一一当确知2.5(-)比表中推荐尺寸小得多时，可米用较小试件. 在试验 0.2 K 测得有效K IC结果后，可在随后试验中将尺寸减少到a、B 2.5( -)2 0.2 B > 2.5(K ic/ 动2>2.5(71.9/294)2=0.l496m 所以取B=0.15m. (2) 高度： a> 50r y~ 2.5(K ic/『① (W-a) > 2.5(K ic/ s)2C2) 由O+②得W 2*2.5(K ic/ s)2 ,所以取W=0.3m (3) 长度：跨距：S=4W+0.2W=1.26m. 长度L>S,所以取L=1.4m。为了模拟实际构件中存在的尖锐裂纹，使得到的K1-数据可以对比和实际应用，试件必须在疲劳试验机上预制疲劳裂纹。预制疲劳裂纹开始时，最大疲劳载荷应使应力强度因子的最大值不超过K1C的80%, 疲劳载荷的最低值应使最低值与最小值之比在-1与0.1之间。在疲劳裂纹扩张的最后阶段，至少在2.5%a的扩展中，应当减少最大载荷或位移，使疲劳应力强度因子的最低值 K fmax w 0.6K 1c, K fmax/E<0,0032m 1/2。同时调整最小载荷或位移，使载荷比乃在-1~0.1之间。

断裂韧度与钢组织性能的关系

2007年11月第2卷第4期失效分析与预防 N ove m ber ,2007V o.l 2,N o .4 [收稿日期] 2007年2月26日 [修订日期] 2007年3月28日 [作者简介] 郭峰(1982年-),男,硕士研究生,主要从事金属材料方面的研究。断裂韧度与钢组织性能的关系郭峰,李志 (北京航空材料研究院,北京 100095) [摘要] 本文阐述了断裂韧度与材料本征因素和基本力学性能的关系。合金成分、微量元素、夹杂物和第二相、显微组织与晶粒度是控制断裂韧度的关键因素,提出了改善断裂韧度的一些思路和方法,如改善晶界状态、细化晶粒尺寸、控制夹杂物的含量、变性变质夹杂物、改善材料组织结构都能改善材料的断裂韧。断裂韧度既是强度、塑性、冲击韧性的综合反映,同时具有独立的力学意义,断裂韧度与材料力学性能之间的关系使经济、有效地预测断裂韧度成为可能。[关键词] 断裂韧度;材料因素;力学性能 [中图分类号] O346.1 [文献标识码] A [文章编号] 1673-6214(2007)04-0059-06 Correl ation between K I C and M icrostructure and Properties of Steels GUO Feng ,LI Zhi (B eijing Institute of A eronauticalM aterials ,B ei j i ng 100095,Ch i na) Abstrac t :In t h i s paper ,the re l ations a m ong fract ure t oughness ,the essential factors and the basic m echan i ca l properti es of the m ater i a ls are i ntroduced .The key factors o f a ffecti ng t he facture toughness a re all oy com ponent ,m icro ele m ent ,i nclus i ons ,the second phases ,m i crostructure and the g ra i n size .Som e thoughts and me t hods tha tm ay i m prove t he fracture toughness o f the ma -ter i a l s are put f o r w ard ,for exa m ple ,am end i ng the state of the g ra i n i nte rface ,m aki ng t he gra i n size s m a l,l controlling t he con -tent o f t he i nclusi ons ,chang i ng the i ncl usion estate ,i m prov i ng the m ater i a lm icrostruct ure and so on .F rac t ure t oughness is not on l y t he i nteg rated refl ection of streng t h ,plasti c and i m pact toughness o f the m ater i a ls ,but a lso a spec ialty mechan i ca l property .T he relation bet ween the fracture toughness and o t her m echanical properti es m ake it possi ble to forecast the fracture toughness e -conom i ca lly and effec tive l y . K ey word s :fract u re t oughness ;m ate rials factors ;mechan i ca l property 1 引言金属材料的失效是由于材料表面或内部裂纹(群)的萌生和扩展,随着裂纹的扩展,裂纹前端的应力强度因子将达到临界应力强度因子,即材料的断裂韧度 ,裂纹将迅速扩展而导致材料抵抗断裂的能力下降和丧失。因此,研究断裂韧度的影响因素,对于失效分析和预防有重要意义。 Griffth 于1920年根据能量原理提出的断裂准则表明:当裂纹扩展释放的能量超过了相同裂纹增量所需的表面能时,裂纹将失稳扩展。30年后,O ro w an 通过对金属材料裂纹扩展的研究,指出裂纹扩展尖端产生一个塑性区。因此,在G rif-f th 判据基础上,提出塑性功和表面能成为裂纹失稳扩展的阻力。众所周知,实际材料总是不可避免地带有裂纹缺陷或容易产生裂纹缺陷,这样,在设计材料时必须考虑已具有裂纹的条件下的力学性能指标即断裂韧度。平面应变断裂韧度K I C 是在断裂力学的基础上建立起来的表征实际含裂纹构件抵抗裂纹失稳扩展的力学性能指标,其物理意义表示平面应变临界强度因子,即平面应变条件下,构件在静载荷作用下裂纹开始失稳扩展的K I (张开型裂纹的临界应力强度因子)。

金属的断裂韧度

第四章金属的断裂韧度断裂是工程上最危险的换效形式。特点：（a）突然性或不可预见性；（b）低于屈服力，发生断裂；（c）由宏观裂扩展引起。 ∴工程上，常采用加大安全系数；浪费材料。但过于加大材料的体积，不一定能防止断裂。 ∴发展出断裂力学断裂力学的研究范畴：把材料看成是裂纹体，利用弹塑性理论，研究裂纹尖端的应力、应变，以及应变能力分布；确定裂纹的扩展规律；建立裂纹扩展的新的力学参数（断裂韧度）。主要内容：含裂纹体的断裂判据。固有性能的指标—断裂韧性：用来比较材料拉断能力，K IC ,G IC , J IC ,δ C 。用于设计中： K IC 已知，σ，求a max K IC 已知 , a c 已知，求σ构件承受最大承载能力。 K IC 已知，a已知，求σ。讨论：K IC 的意义，测试原理，影响因素及应用。 §4-1线弹性条件下的断裂韧度一、裂纹扩展的基本形式 1、张开型（I型） 2、滑开型（II型） 3）撕开型（III型）裂纹的扩展常常是组合型，I型的危险性最大二、应力场强度因子KI和断裂韧度K IC 。 1、裂纹尖端应力场，应力分析 ①应力场离裂纹尖端为(，)的一点的应力：（应力分量，极座标）

平面应力 σx =0 平面应变 σx =υ（σx +σy ）对于某点的位移则有平面应力情况下位移平面应变情况时，上式为平面应变状态，位移分量。越接近裂纹尖端（即r 越小）精度越高；最适合于r<