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Effect of manufacturing defects on mechanical properties and failure features of 3D orthogonal woven C/C

composites

Ai Shigang a ,Fang Daining b ,?,He Rujie b ,1,Pei Yongmao b

a Institute of Engineering Mechanics,Beijing Jiaotong University,Beijing 100044,PR China

State Key Laboratory of Turbulence and Complex System,College of Engineering,Peking University,Beijing 100871,PR China

a r t i c l e i n f o Article history:

Received 8September 2014

Received in revised form 1November 2014Accepted 3November 2014

Available online 10November 2014Keywords:

A.Carbon-carbon composites (CCCs)

B.Defects

C.Damage mechanics C.Numerical analysis

D.Non-destructive testing

a b s t r a c t

For high performance 3D orthogonal textile Carbon/Carbon (C/C)composites,a key issue is the manufac-turing defects,such as micro-cracks and voids.Defects can be substantial perturbations of the ideal archi-tecture of the materials which trigger the failure mechanisms and compromise strength.This study presents comprehensive investigations,including experimental mechanical tests,micron-resolution computed tomography (l CT)detection and ?nite element modeling of the defects in the C/C composite.Virtual C/C specimens with void defects were constructed based on l CT data and a new progressive dam-age model for the composite was proposed.According to the numerical approach,effects of voids on mechanical performance of the C/C composite were investigated.Failure predictions of the C/C virtual specimens under different void fraction and location were presented.Numerical simulation results showed that voids in ?ber yarns had the greatest in?uences on performance of the C/C composite,espe-cially on tensile strength.

1.Introduction

Carbon ?ber reinforced carbon composites (C/C)have high ther-mal stability,thermal shock resistance,strength and stiffness in non-oxidizing atmosphere.Due to its superior speci?c strength and toughness,C/C composites can be considered as favourite materials for highly demanding thermostructural lightweight applications e.g.in aerospace and nuclear industry [1–6].Nowa-days C/C components are leading candidates for applications under extreme conditions.C/C composites are produced by chemical vapor in?ltration (CVI)of a textile ?ber preform.After the CVI pro-cess and high temperature heart-treatments,generally,manufac-turing defects exist inner the materials.In particular,porosity/voids and micro-cracks are typical defects in C/C composites,and seriously affect the performance of the composites [7–9].So,it is mandatory to account for the effects of defects and their evolution,even in the early stages of the design process.With the increasing use of C/C composites as advanced structural materials,the deter-mination of damage criticality and structural reliability of compos-ites has become an important issue in recent years.

Defects–mechanical property relationships of ?ber reinforced composites have always been of interest to scientists addressing the composite performance.In Gowayed et al.’s work [10],defects in an as-manufactured oxide/oxide and two non-oxide (SiC/SiNC and MI SiC/SiC)ceramic matrix composites were categorized and their volume fraction quanti?ed using optical imaging and image analysis.Aslan and Sahin [11]investigated the effects of delamin-ations size on the critical buckling load and compressive failure load of E-glass/epoxy composite laminates with multiple large del-aminations by experiments and numerical simulations.In Masoud et al.’s work [12]effects of manufacturing and installation defects on mechanical performance of polymer matrix composites appear-ing in civil infrastructure and aerospace applications were studied.Damage onset and propagation were studied used time-dependent nonlinear regression of the strain ?eld.In Refs.[13–17],the ?nite element method (FEM)was followed by various authors to study the delamination problems.FEM is preferred than analytical solu-tions because it can handle various laminate con?gurations and boundary conditions.

In recent decades,high-?delity X-ray micro-computed tomog-raphy (l CT)technology has been used to characterize defects and reconstruct meso-structure of textile composites [18].In Cox et al.’s work [19–21],three-dimensional images of textile com-posites were captured by X-ray l CT on a synchrotron beamline.Based on a modi?ed Markov Chain algorithm and the l CT data,

?Corresponding author.

E-mail addresses:sgai@https://www.wendangku.net/doc/7110488221.html, (F.Daining),rujh@https://www.wendangku.net/doc/7110488221.html, (H.Rujie).1

Co-corresponding author.

a computationally ef?cient method has been demonstrated for generating virtual textile specimens.In Fard et al.’s work [22],manufacturing defects in stitch-bonded biaxial carbon/epoxy composites were studied through nondestructive testing (NDT)and the mechanical performance of the composite structures was investigated using strain mapping technique.In Desplentere et al.’s work [23],X-ray l CT was used to characterize the micro-structural variation of four different 3D warp-interlaced fabrics.And the in?uence of the variability of the fabric internal geometry on the mechanical properties of the composites was estimated.In Guillaume et al.’s work [24]effects of porosity defects on the interlaminar tensile (ILT)fatigue behavior of car-bon/epoxy tape composites were studied.In that work,CT mea-surements of porosity defects present in specimens were integrated into ?nite element stress analysis to capture the effects of defects on the ILT fatigue behavior.In Thomas et al.’s work [25]X-ray microtomography technology was adopted to measure the dimensions and orientation of the critical defects in short-?ber reinforced composites.Generally,geometry reconstruction based on l CT data is a huge and complex work,sometimes,virtual specimens explored through this approach are dif?cult to use for numerical analysis.For 3D fabric composites,because of the 2.Material and experiments

Material studied in this article is C/C 3-D orthogonal woven ceramic composite (fabricated by National Key Laboratory of Ther-mostructure Composite Materials,Northwestern Polytechnical University,China)in which T300carbon ?ber (Nippon Toray,Japan)tows rigidi?ed by carbon matrix.The C/C composite was prepared using chemical vapor in?ltration (CVI)method.T300car-bon ?ber was used as reinforcement of the C/C composites with the ?ber volume fraction was 56.5%.The ?ber preforms,as shown in Fig.1a,were in?ltrated with carbon matrix using multiple cycles of in?ltration and heat treatment at 1373K,0.03MPa (the thick-ness of the ?ber preforms is about 5mm).With increasing cycles,a matrix with near full density can be asymptotically approached,generally,it was about 10cycles (1200h).The C/C specimens are illustrated in Fig.1b (the thickness of the tensile specimen is 5.0mm).However,from the l CT images of the C/C materials,it was found that manufacturing defects such as voids and micro-cracks appeared inner the composites.It is because of the special material preparation process.The manufacturing defects are illus-trated in Fig.1c.

Uniaxial tensile experiments were carried out under a Shima-Fig.1.C/C 3-D orthogonal woven composite.

Fig.2.Stress–strain curve of the C/C composite under uniaxial tension.

114 A.Shigang et al./Composites:Part B 71(2015)113–121

In the tensile experiments,?ve specimens in total were tested and the tensile strengths were217.3,185.1,219.8,176.5and 187.3MPa correspondingly.The average value of the tensile strength was197.2MPa and the dispersion of the experimental results was less than11.5%.Other more,the fracture behaviors of the?ve specimens were similar with the failure locations almost all located in the middle of the specimens.From the experiments, deformation of the C/C3-D orthogonal composite under uniaxial tension comprises with three stages:linear elastic stage,damage initiation/evolution stage and the material fracture stage.In the ?rst stage the stress–strain curve increased linearly and in the sec-ond stage the stress–strain curve increased nonlinearly.In the frac-ture stage the stress–strain curve rapidly declined.

3.Numerical programmer

3.1.3D?nite element model

Fiber tows in the3-D orthogonal architectures?t together snugly in the woven pattern by a system of periodic motions, and approximately in the same cross-sectional geometry.In this study,cross-sections of the warp?ber yarns and weft?ber yarns were?tted as rectangle.The cross-sections of the z-binder tows were?tted as circular.Geometric parameters of the?ber yarn cross-sections were recorded.For the warp yarns and weft yarns the side lengths of the cross-section rectangle were0.786mm and0.340mm.For the z-binder?ber yarns the diameter of the cross-section circular was0.790mm.The smallest repeatable rep-resentative volume element(RVE)of the textile architecture was constructed and shown in Fig.3.The lengths of the RVE model in X and Y direction both were1.96mm and the height of the RVE model in Z direction was0.76mm.

To reveal the internal defects in the?nite element model,l CT technology was used to investigate the meso-structures of the fore,three local coordinates were constructed to identify the mate-rial directions.Then,an interface zone with a constant thickness 0.01mm was generated based on the geometrical model of the ?ber yarns,as shown in Fig.3d.Finally,a solid block model with the same size of the composite specimen was constructed.Boolean operation were carried out among the solid block,interfaces and the?ber yarns to generate the geometrical model of the carbon matrix,which is shown in Fig.3b.A whole RVE model of the com-posite is illustrated in Fig.3a.

A Monte Carlo algorithm was adopted to choose elements one-by-one randomly as‘‘void defects’’until the volume fraction of the voids satis?ed the threshold values in the three zones respectively. For the C/C composite studied in this paper,the void fractions of the?ber yarns,matrix and the interfaces are0.51%,0.47%and 1.94%respectively.It must be noted out that those elements which identi?ed as‘‘void defects’’were not moved away from the FE model,but the stiffness was degenerated by10eà6times in the simulation process.The void defects in the three zones are high-light as‘‘red’’,as shown in Fig.3.

3.2.Progressive damage model

The failure criterion proposed here is a strain-based continuum damage formulation with different failure criteria applied for matrix and?ber yarns.A gradual degradation of the material prop-erties is assumed.This gradual degradation is controlled by the individual fracture energies of matrix and?ber yarns,respectively. The?ber yarn is in the X(1)–Y(2)–Z(3)Cartesian coordinate sys-tem,and the X direction corresponds to the?ber longitudinal direction.For the?ber yarns,two different modes of failure are considered:?ber failure in longitudinal direction and matrix fail-ure in transverse direction.The damage mechanism consists of two ingredients:the damage initiation criteria and the damage evolution law.

orthogonal textile C/C composite,(a)RVE model,(b)carbon matrix,(c)?ber yarns and(d)?ber yarns-matrix

interpretation of the references to colour in this?gure legend,the reader is referred to the web version of this

A.Shigang et al./Composites:Part B71(2015)113–121115

failure strains in?ber direction in tension and compression,F f;t

X and F f;c

are the tensile and compressive strength of the?ber

yarns in X direction,respectively.Once the above criterion is sat-

is?ed,the?ber damage variable,f X

,evolves according to the fol-lowing equation law:

d X f ?1à

e f;t

f X

eàC11e f;t11f X fàe f;t11

eTL c=G f

eTe2T

where L c is the characteristic length associated with the material point.For matrix failure the following failure criterion is used:

f Y m ?

????????????????????????????????????????????????????????????????????????????????????????????????????????????????

e f;t

e f;c

ee22T2te f;t22à

e f;t

e f;c

C A e22te f;t22

e f;s

ee12T2>e f;t22

v u

u u

u te3T

f Z m ?

????????????????????????????????????????????????????????????????????????????????????????????????????????????????

e f;t

ee33T2te f;t33à

e f;t

C A e33te f;t33

ee13T2>e f;t33

v u

u u

u te4T

where e f;t22;e f;t33;e f;c22and e f;c33are the failure strains perpendicular to the ?ber direction in tension and compression,respectively.The failure strain for shear are e f;s13and e f;s12.Failure occurs when f Y m exceeds its threshold value e f;t22or f Z m exceeds its threshold value e f;t33.The evolu-tion law of the matrix damage variable,d m,is:d Y

?1à

e f;t

f Y

eàC22e f;t22f Y màe f;t22

eTL c=G m

eTe5T

d Z

?1à

e f;t

eàC33e f;t33f Z màe f;t33

eTL c=G m

eTe6T

As damage progressing,the effective elasticity matrix is

reduced as functions of the three damage variables f X

,d Y

and d Z

, as follows:

3.2.2.Failure criterion for matrix

Damage in the?ber is initiated when the following criterion is reached:

where e f;t and e f;c are the failure strains in tension and compression respectively and e f,t=r f,t/C11,e f,c=r f,c/C11.Once the above criterion

is satis?ed,the?ber damage variable,f XeY=ZT

,evolves according to the equation:

d XeY=ZT

?1à

f;t

eàC11e f;t f XeY=ZT

àe f;t

L c=G m

e9TThe modulus matrix of the matrix will be reduced according to:

In user subroutine UMAT the stresses are updated according to the following equation:

C f d ?

1àd X

C111àd X

1àd Y

C121àd X

1àd Z

C13000

1àd Y

C221àd Y

1àd Z

C23000

1àd Z

C33000

1àd X

1àd Y

C4400

Symmetric1àd X

1àd Z

C550

1àd Y

1àd Z

C66

e7T

f XeY=ZTm ?

??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

f;t

f;c

ee11e22=33TT2te f;tà

ee f;tT2

f;c

e11e22=33Tt

f;t

f;s

ee12e23=13TT2t

f;t

f;s

ee13e12=23TT2

v u

u t

>e f;te8T

C m d ?

1àd X

C111àd X

1àd Y

C121àd X

1àd Z

C13000

1àd Y

C221àd Y

1àd Z

C23000

1àd Z

C33000

1àd X

1àd Y

C4400

Symmetric1àd X

1àd Z

C550

1àd Y

1àd Z

C66

e10T

116 A.Shigang et al./Composites:Part B71(2015)113–121

r ?C d :e

To improve convergence,a technique based ization (Duvaut–Lions regularization [27])of is implemented in the user subroutine.In this age variables are ‘‘normalized’’via the _d t ;X eY =Z Tf em T

?1g

d X eY =Z Tf em Tàd t ;X eY =Z Tf em T

where d X f and d X eY =Z T

m are the ?ber and matrix culated according to the damage evolution d t ;X f and d t ;X eY =Z Tm are the ‘‘normalized’’the real calculations of the damaged elasticity bian matrix,and g is the viscosity parameter.and d t ;X eY =Z T

m can be calculated according to the d t ;X eY =Z Tf em T

t 0tD t

?D t t 0tt d X eY =Z Tf em T t 0tD t tg g tt d

t ;X eY =f em TTherefore,for the ?ber yarns and matrix,can be further formulated as Eqs.(14)and (15)correspondingly

@r e ef T?C f d t@C f d

@d f

:e !@d X f @f f á@f X

!t@C f d @d Y m :e !@d Y m @f Y m á@f Y m @e !t@C f d @d Z m :e !@d Z m @f Z

m á@f Z m

@e !e14T

@r @e em T?C m d t@C m

d @d m :

e !@d X m @

f m á@f X m

t@C m

d @d m :

e !@d Y m @

f m á@f Y m @e !

t@C m d @d m :e !@d Z m @f m á@f Z m @e

!e15T

3.3.Material parameters

3D orthogonal C/C composites are composed by T300?ber yarns and carbon matrix.The ?ber yarns can be regarded as unidi-rectional ?ber-reinforced C/C composites and are assumed to be one transversely isotropic entity in each local material coordinate system.The mechanical properties of the ?ber yarns can be calcu-lated using the properties of the component materials (?bers and matrix):

E 1?e E f 11te1àe TE m

E 2?E 3?E m

1à??e p 1àE m =E f 22eTG 12?G 13?G m 1à?p 1àG m =G f 12eT

G 23?G m

1à?p 1àG m =G f

23eTl 12

?l 13?e l f 12te1àe Tl m l 23

?E 22

2G 23à1

>>>>>>>>>>>>=

>>>>>>>

>>>>>;e16T

where e is the yarn pack factor,for the C/C composite studied in this paper,e =0.81.E f 11,E f 22are the Young’s elastic modulus of the ?ber

in the principal axis 1and 2,respectively.Axis 1is the longitudinal direction of the ?ber yarns.G f 12,G f 23are the shear modulus of the ?ber in the 1–2and 2–3plane,respectively.l f 12is the primary Pois-son’s ratio of the ?ber,E m ,l m and G m represent the Young’s elastic modulus,Poisson’s ratio and shear modulus of the matrix,respec-tively.Materials parameters are listed in Table 1.

It should be noted that the mechanical parameters of the carbon matrix and the T300?bers changed after the CVI process.In particular,strength of the ?ber will had a greater decline.The tensile and com-pressive strength of the T300?ber yarns were tested with the values listed in Table 1.The elasticity modular of the carbon matrix was tested by a nanoindentor system,which developed by Fang’s research team from Peking University [28].In the carbon matrix modular tests,the experiments repeated 20times for statistical averaging.The val-ues in the 20measurements were 7.18,9.77,8.58,10.01,11.92,5.30,9.98,8.14,8.63,7.31,6.19,10.69,11.10,13.45,9.15,9.13,11.27,9.20,10.14and 10.06GPa;average value was 9.36GPa.Mate-rial parameters of the ?ber/matrix interface are not very clear so far,in this study the Young’s elastic modulus and Poisson’s ratio of the inter-faces were assumed as same as the carbon matrix.

G f is one of the key parameters which control the failure pro-gress of the ?ber yarns,however,different values were recom-mended in reported articles.In this study,in?uences of G f on the mechanical properties of the C/C composite were investigated ?rstly.Based on the values reported in Refs.[29,30],?ve virtual specimens with different G f values (0.5,2.0,6.0,10.0,14.0)were constructed and numerical tested.Simulation results were com-pared with the experimental result,as illustrated in Fig.4.It was found that G f has in?uences on tensile strength and fracture strain of the C/C composite.When G f were 0.5,2.0,6.0,10.0and 14.0,ten-sile strengths of the specimens were 200.5,205.1,205.3,214.2and 214.8MPa.When G f were 0.5,2.0,6.0,the failure strains were 0.36%,0.43%and 0.57%correspondingly.When G f is bigger than 10.0,failure strains of the C/C specimens were bigger than 1.0%.So,by the simulation results,in the present study the value of G f was set to 6.0.

Table 1

Materials parameters.

E 11(GPa)

E 22(GPa)?12G 12(GPa)G 23(GPa)

F t (MPa)F c (MPa)S (MPa)

G f (m )(N/mm)g

T300?ber 23040

0.2624

14.3

89075650 6.00.001C matrix 9.360.338210050 1.00.001Interface

9.36

0.33

100

1.0

0.001

Fig.4.Stress–strain curves of the C/C virtual specimens under different G f .

4.Simulation results and discussion

The anisotropic damage model of the?ber yarns and the isotro-damage model of the matrix and the interface were carried

material constitutive equations by User subroutine UMAT ABAQUS nonlinear?nite element codes.Static uniaxial tensile sim-ulations were carried out.In order to keep forces continuity and displacements compatibility of the opposite faces of the unit cell, periodic boundary conditions were imposed in the simulation. Because the opposite faces of the unit cell have the same geomet-rical features,the nodes on the faces were controlled in the same position to form the corresponding nodes in the process of meshing.The periodic BCs were imposed on the corresponding nodes by FORTRAN pre-compiler code,detailed in Ref.[26].The RVE model subjected to a constant displacement load in Y direction and the loading strain is1%.4.1.Effects of the void defects

In order to investigate the void defects on the mechanical prop-erties and failure behaviors of the C/C composite,two RVE models of the C/C composite were numerical simulated.In one RVE model (FE_D),the?ber yarns,interface and matrix all had void defects with the void fractions are0.51%,1.94%and0.47%respectively. For the other RVE model(FE_Intact),no defect inside.The stress–strain curves of the C/C composite in the simulations and experi-ment are illustrated in Fig.5.By the experimental results,the elas-ticity modular of this C/C composite was58.4GPa.By the numerical simulations,for the intact model,the elasticity modular was56.6GPa;for the‘defected’model the modular was56.3GPa. In the view of modular,the simulation error of the two models were3.1%and3.6%compared with the experimental results.The difference between the two FE models was only0.53%,so,void defects have relatively limited effects on the elastic modular of the C/C composite.The uniaxial tensile strength of the C/C compos-ite was197.2MPa by the experiments.In the simulations,the ten-sile strengths were231.4MPa and205.3MPa corresponding to the intact model and the‘defected’model.It was about17.3%and4.1% difference compared with experimental results.It is clear that,the

Fig.5.Stress–strain curves of the C/C composite under uniaxial tension.

Fig.6.Damage evolution in?ber yarns,(a)RVE model with voids defects,(b)intact model.

Part B71(2015)113–121

yarns are corresponding to the three pictures‘o’,‘p’and‘q’in Fig.6. For the RVE model with defects,it was found that damages were ?rstly generated besides the defects.During the loading process, damages were growing in several sections in the?ber yarns.How-ever,for the intact model,damages were almost generated in one section in the?ber yarns.

Damage evolution in carbon matrix and the interface zone are illustrated in Figs.7and8.From the simulation results,in all of the three zones,damages were?rstly generated in the‘defected’RVE model.For the‘defected’model,when e=0.27%damages appeared in the interface zone,while for the intact model the strain was0.33%.In the matrix zone,the strains in the two models were0.31%and0.33%,respectively,when damages appeared.In ?ber yarns,the strains when damages appear for the two models were0.37%and0.44%.So,because of the internal defects,in load-ing progress damages will generate early inner the material.Fail-ure strain of the materials which with defects is comparatively small when compared with the materials without defects.

4.2.In?uence of void location

By the l CT images,it is clear that voids and micro cracks exist in ?ber yarns,carbon matrix and the interface zones.By statistical analysis for those defects,fraction of the voids in those three zones was calculated.To study the in?uence of void location on the mechanical properties of the C/C materials,three?nite element

Fig.7.Damage evolution in carbon matrix,(a)model with voids defects,(b)intact model.

Fig.8.Damage evolution in interface,(a)model with void defects,(b)intact model.

models were constructed and numerically analyzed.In the three RVE models,one model has defects only in the?ber yarns(FE_DF) and another model has the defects only in carbon matrix(FE_DM), while the other one has defects only in the interface zone(FE_DI). Simulation results were compared with the experimental results. Stress–strain curves in the numerical simulations and experiments are illustrated in Fig.9.

Tensile strength calculated by the simulations were208.5MPa, 229.7MPa and230.1MPa,corresponding to the three?nite ele-ment models:FE_DF,FE_DI and FE_DM.By the simulation results of the?nite element models FE_D and FE_Intact,as mentioned in above section,the tensile strengths were205.3MPa and 231.4MPa.It can give the conclusion that,defects in?ber yarns has the biggest effects on the mechanical properties of the C/C composite.If the?ber yarns are perfect and defects only exist in carbon matrix and interfaces,void defects have limited in?uences on the mechanical properties of the C/C composites under the cur-rent void volume fractions.

4.3.In?uence of void volume fraction

By the statistical analysis in Section3.1,volume fractions of voids in the?ber yarns,matrix and the interface zones are0.51%, 0.47%and1.94%.Under this defect fraction,as calculated in Section

,tensile strength of the C/C composite declined12.7%compared with the material which contains no defects.So,it is important and meaningful that if we can make sure about the mechanical behav-iors of C/C composites when we exactly know the void defect frac-tion.If so,it will be helpful for the performance evaluation of C/C composites and structures.

To investigate the in?uence of the void defect fraction on the mechanical performance of the C/C composite,?ve RVE models were constructed and the defect fractions of the?ber yarns were 0.25%,0.5%,1.0%,2.0%and4.0%.In this study,void defect was assumed only exist in?ber yarns.Because,as calculated in Section 4.2,voids in carbon matrix and interfaces zone had very little effects on the mechanical properties of the C/C composite.Uniaxial tension simulations were carried out and the stress–strain curves of the?ve C/C virtual specimens are illustrated in Fig.10.

From the simulation results,it is clear that as the defect fraction increased tensile strength of the C/C composite decreased.For the intact FE model,the tensile strength was231.4MPa.For the?ve FE models with voids defects,the tensile strengths were214.8MPa, 206.6MPa,197.1MPa,182.3MPa and152.8MPa.For the FE model under the defect density0.25%,tensile strength decreased7.2% compared with the intact model.So,if there exist defects inner the C/C materials,even if the volume fraction of the defects was small,it will has obvious effects on the mechanical performance of the composite,especially on the tensile strength.When the defect density was4.0%,tensile strength of the C/C virtual speci-men declined33.9%compared with the intact specimen.

5.Conclusion

Uniaxial tensile properties and meso-structure of the3D orthogonal C/C composite were studied by experimental approaches.Manufacturing defects inner the C/C composite were investigated though a micron-resolution computed tomography (l CT)approach.From the l CT photos of the3-D orthogonal car-bon/carbon composite,it was found that voids and microcracks are two classic type of manufacture defects inner the C/C materials. Base on the statistical analysis of the l CT data,?nite element mod-els of the C/C composite were constructed.According to a new pro-gressive damage model,failure behaviors and mechanical properties of the C/C composites were studied by ABAQUS code. Effects of the void defects on the mechanical performances of the C/C material were numerically investigated.From the numerical simulation results,manufacturing defects such as voids have great effects on the mechanical performance of the carbon/carbon com-posite,especially on the tensile strength.With0.51%void volume fraction,tensile strength of the carbon/carbon composite has 13.2%declines compared with the intact material.When void defects exist in?ber yarns,even if the volume fraction of the defects is small it still will has great in?uence on tensile strength of the C/C composite.However,the defects which exist in carbon matrix and interface have limited effects on the mechanical prop-erties of the C/C materials.So,keep the continuity and improve the density of the carbon?ber yarns in C/C composite manufacture process is the key to improve the mechanical properties of the C/ C composites.

Acknowledgements

Financial support from the National Natural Science Founda-tions of China(Nos.11202007,11232001,11402132)and the Foundation of Beijing Jiaotong University(KCRC14002536)are gratefully acknowledged.

Fig.9.Stress–strain curves of the C/C composite in experiment and simulations.

10.Stress–strain curves of the virtual specimens with different void defect

fraction.

Part B71(2015)113–121

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竹子的力学特性

选题：从力学观点分析竹子的力学特征徐锴，材料1302,2013012057 【摘要】本文通过分析竹子的材料和构造，说明竹子的强度特性。并通过该种特性进行一些实际应用设计，本文选用建筑中的应用。【关键词】竹子，强度，建筑，可持续发展 1、收集的常识【1】：（1）竹,禾本科，竹木质化,有明显的节,节间常中空，高大、生长迅速,竹枝杆挺拔，修长。（2）分布于热带、亚热带至温带地区，其中东亚、东南亚和印度洋及太平洋岛屿上分布最集中，种类也最多。（3）在竹材研究方面，国内外对竹材的物理性质研究的较多，研究重点主要集中在密度、吸水率及干缩性等方面。密度在很大程度上决定着竹材的力学性质，密度主要取决于纤维含量、纤维直径及细胞壁厚度，密度随纤维含量增加而增加。 2、分析竹子强度特性【2】相比较于钢材，竹子体轻,但是硬度大。根据实验测定, 竹材的形变量非常小, 弹性和韧性却很高, 顺纹抗拉强度170M Pa, 顺纹抗压强度达80M Pa。特别是刚竹, 其顺纹抗拉强度最高竟达280M Pa, 几乎相当于同样截面尺寸材的一半。虽然钢材的抗拉强度为一般竹材的2.5～3倍，但若按单位重量计算抗拉能力，则竹材要比钢材强2～3倍。 3、竹强度大的力学分析 3.1 空心圆截面的强度分析【4】

（1）根据化工设备机械基础的弯曲强度理论【4】, 杆件强度主要指标是弯曲应力。弯曲强度条件为 ][W M max max σσ≤=。要提高杆件的强度, 除了合理安排受力, 降低M max 的数值以外, 主要是采用合理的截面形状, 尽量提高抗弯截面模量W 的数值, 充分利用材料。，实心圆截面和空心圆截面的抗弯截面模量分别是 3d 321W π=实)1(32 1W 43απ-=D 空式中, d 是实心杆直径, D 是空心杆外径, 1D 是空心杆内径。2 1D D = α为空心杆内、外径比值, 当空心杆和实心杆的截面积相同时）（2122D -D 4 1d 41ππ=或212D -D d = 则11-1-1D 32 1d 321W W 22433>+==α ααππ）（空实（1）根据以上分析, 空心圆截面杆的抗弯强度比同样截面积的实心杆大; 并且空心圆截面杆内、外直径的比值α越大,其抗弯强度也随之增大。例如, 当α= 0。 7 时, 它的抗弯强度比同样重量的实心圆截面大2倍。因为, 杆件抗弯时从正应力的分布规律可知在杆截面上离中性轴越远, 正应力越大, 而中性轴附近的应力很小, 这样其材料的性能未能充分发挥作用。若将实心圆截面改为空心圆截面, 也就是将材料移置到离中性轴较远处, 却可大大提高抗弯强度。（2）在风荷载下，竹子主要抵抗的是弯矩和剪力。对于抗弯，边缘最大正应力与截面的截面惯性矩I 成反比，而I 随截面半径增大而增大，故空心结构形成的大半径有利于降低边缘最大正应力提高抗弯能力。 3.2 材料分布的强度分析（1）由于边缘的正应力最大，故将优质材料布置在边缘是最优化的结构布置，竹子就做到了这点：竹壁自外而内，分为竹青、竹肉和竹黄三个部分，竹子的表面呈现出青色的叫竹青，由抗拉强度很高的纤维质构成。（2）对于抗剪，竹节又起到了关键的作用。坚硬实心的竹节将竹身分成小段的区格，在每个区格的端部提供可靠的变形约束，从而也能大大提高竹子的抗剪力能力。 3.3 阶梯状变截面的强度分析（1）竹子在风载作用下各段抵抗弯曲变形能力基本相同, 相当于阶梯状变截面杆, 是一种近似的“等强度杆”。（2）因为在风力作用下, 沿杆自上而下各截面的弯矩越来越大。竹子根部所受弯矩最大, 因而根部最粗, 自下而上各截面弯矩越来越小, 竹子也就越来越细。（3）另外, 竹节不仅能够增强竹子的抗弯强度, 同时,能大大地提高竹子横向的抗挤压和抗剪切的能力。 4、竹子最为建筑用材在实际中的应用 4.1 背景：中国是世界上最大的产竹国。竹子生长快，成材早产量高、用途广。据竹材研究者介绍，竹子的生长速度非常快，比其他木材的生长速度都要快。竹子最快的生长速度是24小时长长

体育运动中踝关节损伤的生物力学研究新进展

体育运动中踝关节损伤的生物力学研究新进展体育运动中踝关节损伤很常见，国内外对踝关节的生物力学特性及其影响因素有很多报道，本文就体育运动中踝关节损伤的生物力学研究新进展进行综述。标签：踝关节；生物力学；体育运动中图分类号R322.7 文献标识码 A 文章编号1674-6805(2012)18-0139-02 踝关节损伤在体育运动中很常见。据近期文献[1]报道，在所有体育运动相关的损伤中，踝关节损伤约占25%。踝关节损伤以韧带损伤为主，Fong等[2]调查指出体育运动中踝关节韧带损伤率约占踝关节总体损伤率的80%。踝关节的损伤不仅会影响运动员的正常比赛及训练，如处理不当还会产生踝关节不稳以及退变性骨关节炎等慢性损伤。踝关节损伤机制的研究一直都为国内外运动医学研究的重点，近年来，随着生物力学新技术的出现，国内外对踝关节着陆伤机制的研究也有了更好的理解。本文就体育运动中踝关节着陆损伤的相关生物力学文献综述如下。 1踝关节容易发生损伤的解剖学基础踝关节包括胫距、胫腓和距腓三个关节面，主要保证足部背伸、跖屈、翻转、旋转的功能。胫腓骨远端的内踝、外踝共同行成的踝穴，距骨和踝关节内外侧不能完全匹配，这是踝关节容易发生旋转的解剖学基础。在跳起着陆过程中，踝关节逐渐从跖屈位变换到背伸位，在此过程中踝关节面间的接触面积不断增加，而单位面积受力不断减少，在着陆稳定时，距骨内外侧关节面与胫腓骨间的接触面积最大[3]。踝关节的稳定与韧带的关系密切。踝关节外侧有外侧韧带加固，它起自外踝，分三束止于距骨前外侧、外侧和距骨后方，被分别称为距腓前韧带﹑跟腓韧带和距腓后韧带。外侧韧带是踝部最薄弱的韧带，也是着陆过程较易损伤到的结构。踝关节内侧有强大而坚韧的三角韧带加固。三角韧带的解剖结构多而细小，其维持关节生物力学稳定的机制复杂。Boden等[4]认为，踝关节的稳定性主要依赖于内侧结构、外侧结构和下胫腓联合的稳定性，此三个结构中有两个是稳定的，则踝关节稳定。在踝关节处于跖屈或背屈位时，三角韧带对踝关节及小腿的旋转稳定性会起到非常重要的作用。Michelson等[5]认为踝关节处于极度背伸和跖屈位时，踝关节均内翻，而三角韧带可以有效限制距骨外旋而保证踝关节的稳定。 2踝关节损伤的生物力学研究进展 2.1生物建模与三维有限元采用生物建模来对足部的应力分布进行研究可以为踝关节落地损伤提供足部生理学和病理学方面的证据。建立适当的踝关节生物力学模型成为足部生物力学研究的重点。三维有限元技术可以利用CT或MRI扫描技术获取正常踝关节的各种三维坐标值，然后输入有限元分析软件而建立起踝关节的有限元模型。它不仅可以有效地仿真人体骨骼肌肉系统，还可以推测内部骨组织及软组织的应力分布变化[6]。同传统生物力学的研究相比，三维有限元法还具有费用低、应用广、适应性强的优点。陶凯等[7]运用三维有限元模型量化了不同姿势下的足底压力分布、踝关节内部软组织应力分布以及跳起着陆时足弓的变形对足部生物力学特性的影响。Cheung等[8]运用MRI图像建立了高度解剖学相似的踝部有限元

关于损伤力学的建议与看法

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骨盆环损伤治疗的生物力学研究

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实验一冲击力模拟实验一、实验目的和任务通过开展冲击力仿真实验，学习基于LS-DYNA的有限元基本分析流程和方法，具体包括： 1.对HYPERMESH和HYPERVIEW（或LS-PREPOST）等前后处理软件的使用； 2.掌握保证仿真精度必须关注能量和质量缩放问题； 3.掌握模型调试方法； 4.体会不同材料、高度、速度对冲击力的影响。二、实验仪器和设备软件：LS-DYNA、HYPERMESH、HYPERVIEW（或LS-PREPOST）。硬件：计算机。三、实验步骤 1、模型提交计算与后处理 1)根据提供的初始模型，对文件进行求解计算。 2)查看完成计算所需的时间，ctrl+C，sw2。 3)查看仿真动画。 4)分析该K文件的单位制（mm，ms，kg，kN，GPa）。 2、有限元模型的质量缩放与能量问题 1)设置输出各种能量，*CONTROL_ENERGY。 2)为提高计算效率，增加质量缩放，*CONTROL_TIMESTEP，

DT2MS：-1.112E-06改为-1.112E-03，再改为-1.112E-02，并分别查看并记录所需计算时间，分析该参数对计算效率的影响。讨论如何设置DT2MS的值。 3)查看计算获得的message文件，记录不同DT2MS设置下的质量缩放所引起的质量增加量及百分比。 4)输出总能量、动能、内能和沙漏能（DT2MS：-1.112E-06），根据曲线分析能量转换。 3、输出并分析橡胶垫的冲击力 1)查阅橡胶的材料。 2)查阅车架、撑板、销轴和冲击头的材料。 3)输出冲击头处的冲击力，Contact_mass（CID：1）。 4)输出两根连接销轴的四处接触力，Contact_chejia_zhou_L （CID:3）、Contact_chejia_zhou_R（CID:4）、Contact_chengban_zhou_L（CID:5）/ Contact_chengban_zhou_R （CID:6）。 5)找出系统的最大应力及其出现的位置。 4、下落高度对冲击力的影响 1)修改冲击头距离橡胶垫的高度，初始值为5mm，分别修改为 2mm、10mm和15mm。 2)计算不同高度下落对冲击力的影响。 3)找出系统的最大应力及其出现的位置。 5、输出并分析金属的冲击力

岩石的损伤力学及断裂力学综述

岩石的断裂力学及损伤力学综述摘要：论述了国内外断裂力学及损伤力学的学科发展历程，总结了岩体断裂力学损伤力学的研究内容、研究特点以及岩石力学专家们一些年来所取得的主要成果，并简单介绍了断裂力学损伤力学在岩土工程中的实际应用。最后，通过对岩石破坏的断裂-损伤理论的阐述，指出了综合考虑损伤与断裂的破坏理论是能更好地反映岩石实际破坏过程的一种新的理论, 可在以后的理论研究和实际工程中得以更为广泛的应用。关键词：岩石断裂力学损伤力学应用 1 引言岩石的破坏过程总是伴随着损伤(分布缺陷)和裂纹(集中缺陷)的交互扩展, 这种耦合效应使得裂纹尖端附近区域材料必然具有更严重的分布缺陷。岩石的破坏, 如脆性断裂和塑性失稳, 虽然有突然发生的表面现象, 但是, 从材料损伤的发生、发展和演化直到出现宏观的裂纹型缺陷, 伴随着裂纹的稳定扩展或失稳扩展, 是作为过程而展开的。经典的断裂力学广泛研究的是裂纹及其扩展规律问题。物体中的裂纹被理想化为一光滑的零厚度间断面。在裂纹的前缘存在着应力应变的奇异场,而裂纹尖端附近的材料假定同尖端远处的材料性质并无区别。象裂纹这样的缺陷可称它为奇异缺陷,因此经典断裂力学中物体的缺陷仅仅表现为有奇异缺陷的存在。而损伤力学所研究的是连续分布的缺陷, 物体中存在着位错、微裂纹与微孔洞等形形色色的缺陷,这些统称为损伤。从宏观来看, 它们遍布于整个物体。这些缺陷的发生与发展表现为材料的变形与破坏。损伤力学就是研究在各种加载条件下, 物体中的损伤随变形而发展并导致破坏的过程和规律。事实上, 物体中往往同时存在着奇异缺陷和分布缺陷。在裂纹(奇异缺陷)附近区域中的材料必然具有更严重的分布缺陷, 它的力学性质必然不同于距离裂纹尖端远处的材料。因此, 为了更切合实际, 就必须把损伤力学和断裂力学结合起来, 用于研究物体更真实的破坏过程。 2 断裂力学 2.1 断裂力学学科发展 “断裂力学”指的是固体力学的一个重要分支，该学科要在假定裂纹存在的条件下，寻求裂纹长度、材料抗裂纹增长的固有阻力、以及能使裂纹高速扩展从而导致结构失效的应力之间的定量关系[]1。断裂力学最早是在1920年提出的。当时格里菲斯为了研究玻璃、陶瓷等脆性材料的实际强度比理论强度低的原因，提出了在固体材料中或在材料的运行过程中存在或产生裂纹的设想，计算了当裂纹存在时，板状构件中应变能变化进而得出了一个十分重要的结果：常数≡a c δ。 1949年，奥罗万在分析了金属构件的断裂现象后对格里菲斯的公式提出了修正，他认为产生裂纹所释放的应变能不仅能转化为表面能，也应转化为裂纹前沿

骨盆环损伤的生物力学研究

骨盆环损伤的生物力学研究目的：探讨骨盆环应力走向，为骨盆环损伤提供更可靠、合理的治疗方法。方法：选取6尸体标本第四腰椎及近端股骨在内的完整骨盆，人为应用垂直作用力及旋转作用力作用于骨盆，观察并记录各标记点应变值。结果：随着作用力加大，相关观察点应变值随即变化。结论：骶股弓是骨盆传导垂直负荷的主要途径，耻骨联合分离及外旋力作用易导致骶髂关节损坏。 [Abstract] Objective：To study the stresses trend of the pelvic ring，and to provide more reliable and reasonable treatments for pelvic ring injuries.Method：Complete pelvises in 6 corpse specimen were selected，including the fourth lumbar spine and proximal femur，and researchers used vertical force and rotational force on pelvises，and the strain values of tags were observed and recorded.Result：Related viewpoint strain values changed as the force increased.Conclusion：Sacral shares bow is the main way to transmit pelvic vertical load，and pubic symphysis separation and outward turning force can lead to damage of sacroiliac joints. [Key words] Pelvic rin；Biomechanics；Symphysis separation；Mechanical testing machine 骨盆骨折病情严重，治疗不当的话往往出现较严重的并发症。据文献[1-2]报道，骨盆骨折致死率为5%～20%左右，而致残率却高达50%～60%。因此，本研究通过对标本骨盆进行生物力学研究，为治疗提供一种能有效减少骨折损伤并发症的生物力学依据，现报告如下。 1 材料与方法 1.1 一般材料选取实验室用一年内尸体标准6具，其中男4具，女2具；死亡年龄35～54岁，平均（42.5±8.3）岁。所用标本经X线摄片均未有骨质疏松等骨骼相关疾病。取标本包括腰四及股骨近端三分之一之间的完整骨盆模型，除去皮肤、肌肉、结缔组织，只保留髋关节囊、骨间韧带、耻骨联合及骨盆后方诸韧带。 1.2 方法 1.2.1 单纯垂直作用力将制作好的模具放入夹具内，模拟人体正常站立。以应变花布置测试点，如图1所示，选取20个观察点（骶髂关节两侧）。将模具置于力学实验机上，以10 N/S的垂直作用力作用于模具上，应用应变仪分别记录模具在耻骨联合正常、耻骨联合分离1 cm、2 cm、2.5 cm时模具承受依次100 N/S、200 N/S、300 N/S、400 N/S、500 N/S作用力时的应变值。每个模具实验过程重复三次取平均值。

土体抗拉张力学特性研究现状与展望

土体抗拉张力学特性研究现状与展望：传统非饱和土力学认为来源于土壤学或土壤物理学中的基质吸力就是非饱和土的粒间吸力，下面是小编搜集整理的一篇探究抗拉张力学特性试验的论文范文，供大家阅读参考。 1、引言在传统工程地质环境及土力学性质的研究中，土体通常不主动作为抗拉材料使用，认为土的抗拉强度很小或几乎视为零[1,2],实际工程中土体的抗拉强度常常被忽略，多侧重于抗压和抗剪，对抗拉张的研究较少[3,4].然而，许多工程问题中的土体会发生开裂现象，诸如红色问题土中常见的崩岗[5]、滑坡以及黄土中常见的滑塌[6]等地质灾害孕育过程中坡顶几乎都产生的张拉裂缝[7,8],其破坏模式是拉张和剪切的耦合，都与其抗拉张力学特性密切相关。抗拉张强度是评价非饱和土的崩岗、崩塌及土坝、堤防、路基、垃圾填埋场等边坡的稳定性的重要参数，黄文熙[9]早就指出抗拉张是黏性土的一个比较重要的力学性质。试验研究表明[4,10] 天然非饱和黏性土的抗拉强度一般可达到十几到几十千帕，从抗拉力学角度，土体的抗拉强度几乎相当于同等面积内2m×3m间距锚杆的抗拔力。可见，抗拉强度在土体稳定性中起着相当重要的作用，忽略土的抗拉张强度显然是对土的强度认识上的不全面。本文从土体抗拉张力学特性的实验研究和理论分析2个角度出发，介绍并对比分析了国内外土体抗拉张力学特性的试验以及理论方面的最新研究，通过总结分析历史上大量的岩土破坏试验抽象概括出了土体的8种破坏模式，随后认为土体变形破坏的实质是拉剪耦合的渐进性发展过程，并指出研究非饱和土抗拉特性的核心问题就是要弄清土体抗议与粒间吸力之间的关系，最后总结了研究现状中存在的主要问题，展望了今后的研究与发展方向。 2、抗拉张力学特性试验研究土体的抗拉张力学特性的测试主要在室内进行，分2类：一类是直接测定法，即单轴拉伸试验和三轴拉伸试验方法;另一类是间接测定方法，包括径向压裂试验、弯曲梁试验和环状试样法等。比较土体抗剪特性及理论的研究，土体抗拉张特性的研究程度无论从试验手段还是从理论方面都还是远远落后的。例如，至今仍没有统一规范并获得业界普遍认同的土体抗张特性测试仪器。不过，当前抗拉张的新型试验

荔枝果核力学特性分析及试验

万方数据

荔枝果核力学特性分析及试验作者：程红胜，李长友， Cheng Hongsheng， Li Changyou 作者单位：华南农业大学,工程学院,广州,510642 刊名：农机化研究英文刊名：JOURNAL OF AGRICULTURAL MECHANIZATION RESEARCH 年，卷(期)：2009,31(12) 被引用次数：1次参考文献(12条) 1.刘燕群中国荔枝产业发展现状、问题及对策[期刊论文]-世界农业 2008(03) 2.徐秉业;罗学富接触力学 1992 3.Mohsenin N N Physical properties of plant and animal materials 1970 4.王泽南;单明彻水果机械特性及损伤的研究 1986(03) 5.吴德光;蒋小明农产品压缩试验研究及其应用(Ⅰ)-压缩试验方法 1990(03) 6.周祖锷农业物料学 1994 7.戴晓红荔枝加工机结构设计原理分析[期刊论文]-包装与食品机械 1997(02) 8.王旭东荔枝去核机的设计[期刊论文]-农业机械学报 2005(09) 9.张林泉荔枝剥壳设备的研制[期刊论文]-包装与食品机械 2004(06) 10.陈震荔枝力学特性参数测试研究[期刊论文]-农机化研究 2008(09) 11.王旭东;朱立学;刘江清荔枝物理参数和机械特性的试验研究[期刊论文]-农机化研究 2007(12) 12.袁沛元;蔡长河荔枝加工现状与技术探讨[期刊论文]-中国热带农业 2005(25) 本文读者也读过(10条) 1.贾彦丽.温陟良.吕瑞江.段玉春.智福军.JIA Yan-li.WEN She-liang.LU Rui-jiang.DUAN Yu-chun.ZHI Fu-jun 无核小枣果核发育的解剖学研究[期刊论文]-华北农学报2007,22(z2) 2.陈震.徐凤英.李长友.卢顺成.CHEN Zhen.XU Feng-ying.LI Chang-you.LU Shun-cheng荔枝力学特性参数测试研究[期刊论文]-农机化研究2008(9) 3.陈震.李长友.洪英荔枝力学特性分析与测试[会议论文]- 4.宋慧芝.王俊.陈琦峰.严志权.Song Huizhi.Wang Jun.CHEN Qifeng.Yan Zhiquan梨动力学特性有限元分析[期刊论文]-农业机械学报2005,36(6) 5.徐永春.陈震农业物料力学测试平台系统设计[期刊论文]-现代农业装备2004(9) 6.张洋.王德成.王光辉.刘德旺.王书茂牧草种子机械化加工工艺的分析[会议论文]- 7.刘建军.宋建农.陆建伟.彭樟林.彭何欢.LIU Jian-jun.SONG Jian-nong.LU Jian-wei.PENG Zhang-lin.PENG He-huan大蒜物理力学特性的试验研究[期刊论文]-农机化研究2008(2) 8.杨晨升.马小愚.Yang Chensheng.Ma Xiaoyu农业物料动态力学特性的试验研究[期刊论文]-农机化研究2009,31(4) 9.刘圣勇.王淮东.康艳.李文雅.苏超杰.袁超.朱长河.LIU Sheng-yong.WANG Huai-dong.KANG Yan.LI Wen-ya.SU Chao-jie.YUAN Chao.ZHU Chang-he玉米秸秆成型燃料结渣特性试验与分析[期刊论文]-河南农业大学学报2006,40(6) 10.刘圣勇.李文雅.苏超杰玉米秸秆成型燃料结渣特性实验与分析[会议论文]-2006 引证文献(1条) 1.陈燕.蔡伟亮.邹湘军.徐凤英荔枝整果压缩力学特性试验[期刊论文]-安徽农业科学 2010(29)

损伤力学读书报告

《损伤力学》读书报告随着现代工业的飞速发展，大型机械和复杂构件的日益增加，金属构件的疲劳失效已经成为工程领域中，关系到安全、可靠以及经济性的一个重要因素。一般认为金属的疲劳破坏形式分为如下几个阶段：裂纹形核、小裂纹扩展、长裂纹扩展以及瞬时失效阶段，一般将裂纹形核和小裂纹扩展归为第一阶段，对于这阶段的研究，其主要方法是试验与统计相结合的方法，目前较多的研究室基于细观力学、分子动力学以及断裂物理的研究较多，对于裂纹的扩展阶段，一般是采用试验与断裂力学相结合的方法，这对于飞行器以及工程构件的损伤容限设计是非常必要的手段。但是这些方法也存在于若干不足之处：（1）、对于裂纹的曲线扩展路径的描述困难。（2）、二维裂纹扩展和三维裂纹扩展的描述难以统一。（3）、把第一阶段与裂纹扩展阶段视为独立的阶段。为止，就需要一个新的固体力学工具，将裂纹形成与扩展的描述进行统一，将二维和三维裂纹的扩展研究进行统一，将裂纹的直线扩展与曲线扩展进行统一。此时，损伤力学就应运而生，从80年代初期，到目前为止，这方面出版了许多专著，他们对损伤力学的理论以及发展做出了巨大的贡献；下面就介绍损伤力学的一些先关内容：一、破坏力学的发展及损伤力学定义破坏力学发展的三个阶段 1)、古典强度理论：以材料的强度作为设计指标：[]σσ<*,即只要材料的应力*σ小于材料的许用应力[]σ就不会破坏。 2)、断裂力学：以材料的韧度为设计指标：IC IC J K J K , ,<。 3)、损伤力学：以渐进衰坏程度作为为指标：C ωω<。损伤力学定义损伤力学是研究材料的细(微)结构在载荷历史过程中产生不可逆劣化(衰坏)过程，从而引起材料(构件)性能变化、以及变形破坏的力学规律。二、传统材料力学的强度问题对于传统的力学材料研究首先满足：材料均匀性和连续性假设，即认为材料是各处性质相同的连续体。其研究理论和思想如下图所示：

混凝土断裂损伤力学

混凝土断裂损伤力学随着经济水平的不断提高，土木水利工程建设在世界范围内取得了迅猛发展。混凝土作为土木水利工程中最重要的建筑材料之一，其损伤断裂特性对工程安全起着关键作用。如何准确把握混凝土的破坏机理，确定合理的混凝土断裂参数，对评价混凝土结构的稳定性和安全性具有重大意义。混凝土是由水泥、砂子、石子等经化学反应生成的多相复合材料，它自身的非均匀性以及复杂的内部结构，使得混凝土的断裂破坏机理也非常复杂，如何合理研究其由损伤、断裂到失稳破坏的复杂过程，一直是研究者极为关心的课题。混凝土的破坏过程和机理混凝土是以骨料为填料、以硬化水泥浆为母体组成的复合材料。因此，骨料和硬化水泥浆以及它们结合面的力学特性必然会影响混凝土的力学性能。现代化测试技术和计算技术为我们观察和研究混凝土材料的破坏机理提供了方便。虽然不同的学者由于所采用的观测方法与试验仪器的灵敏度、精度等不同，导致裂缝扩展过程中相应于不同阶段的应力水平并不完全一致，但是所得的结论都证实：未加荷载之前，混凝土中已经有微裂缝存在；在荷载作用下，混凝土的破坏实质上就是裂缝的产生、稳定扩展与不稳定扩展的过程，即裂缝的扩展经历了裂缝起裂、裂缝稳定扩展与裂缝失稳扩

展三个阶段；而且混凝土破坏过程中并非单一裂缝在扩展，另外还有众多的次裂缝。应力-应变关系是混凝土在外力作用下变形及破坏现象的外部表现。在单轴压缩应力状态下，砂浆、骨料以及混凝土典型的应力-应变曲线如图1所示。图1 单轴压缩时的应力-应变曲线比较由图可知，对骨料而言，在达到破坏荷载前，其应力-应变曲线基本上是线性的。砂浆而言，直到破坏荷载的90%~95%之前，其应力-应变曲线也基本上是线性的。但是，混凝土的应力-应变曲线则有明显的不同，在荷载达到抗压极限强度的30%~40%之前，应力-应变曲线接近直线；应力超过该点之后，应力-应变曲线的曲率逐渐增加，当应力达到抗压极限强度的70%~90%时，曲线明显弯曲；应力达到抗压极限强度后，应力-应变曲线达到峰点，可见，混凝土应力-应变曲线形状的变化与其内部裂缝的扩展有着密切的关系。因此，以裂缝的扩展过程为标准，混凝土的破坏过程可分为下面三个阶段。第一阶段准弹性阶段。在30%~40%的极限抗压强度以内，该阶段应力-应变曲线基本呈直线，在施加荷载之前已有的微裂缝处于稳定状态，几乎没有扩展的趋势。除了已存在的裂缝之外，在试件内的某些孤立点上会产生应力集中，使得在应力集中的微小局部区域内也可能引发一些附加裂缝，它们也将保持

力学性能

1、力学性能：材料在力的作用下所表现出来的特性。力学性能包括强度、硬度、塑性、韧性、疲劳特性、耐磨性。强度包括屈服强度和抗拉强度。硬度是指材料抵抗局部塑性变形的能力。测试方法有布氏硬度法、洛氏硬度法、维氏硬度法。布氏硬度优点是测量误差小，数据稳定；缺点压痕大，不能用于太薄件或成品件。洛氏优点操作方便、压痕小、适用范围广；缺点测量结果分散度大。维氏优点可根据工件硬化层的厚薄任意先选择载荷大小，可以测定由软到硬的各种材料。塑性：只材料在外力作用下破坏前可承受最大塑性变形的能力。衡量指标为断后伸长率和断面收缩率。物理性能：密度、熔点、导热性、热膨胀性、磁性。化学性能：耐腐蚀性、抗氧化性。工艺性能指机械零件在冷、热加工的制造过程中应具备的性能，包括：铸造性能、锻压性能、切削加工性能、热处理性能。 2、晶格：描述原子排列方式的空间格架；晶胞：晶格中能代表晶格特征的最小几何单元；晶格常数：晶胞的棱边长度a b c。单晶体：多晶体；晶界：晶粒之间的交界；亚晶界：亚晶粒之间的交界；位错：在晶体中某处有一列或几列一原子发生有规律的错排的现象；位错密度：单位体积中包含的位错线总长度；各向异性：同素异构体转变：在固体下随温度的改变，由一种晶格转变为另一种晶格的现象；试说明缺陷的类型，内容及对性能的影响：1点缺陷：当晶体中某些原子获得足够高的能量，就可以克服周围原子的束缚，而离开原来的位置，形成空位的现象；点缺陷的存在，使晶体内部运动着的电子发生散射，使电阻增大，点缺陷数目的增加，使晶体的密度减小，过饱和的点缺陷可提高材料的强度和硬度，但降低了材料的塑性和韧性。2线缺陷：降低了金属的强度；3面缺陷：晶体中存在的一个方向上尺寸很小，另两个方向上尺寸很大的缺陷；提高了金属的强度和塑性。。。 3、因为金属的实际结晶温度总是低于理论结晶温度，所以总会产生过冷现象；冷却速度越大，过冷度就越大；说明纯金属的结晶过程：总是在恒温下进行，结晶时总有结晶潜热放出，结晶过程总是遵循形核和晶核长大的规律，在有过冷度的条件下才能进行结晶。说明晶粒大小对力学性能的影响：常温下细晶粒金属比粗晶粒金属有更高的强度、硬度、塑性和韧性；生产中控制晶粒大小的方法：（1）提高结晶时的冷却速度、增加过冷度（2）进行变质处理（3）在浇注和结晶过程中实施振动和搅拌，向液体中输入额外能量以提供形核功，促进晶核形成。说明加工硬化对金属性能的影响：（1）提高金属强度、硬度和耐磨性的重要手段之一，特别是对那些不能进行热处理强化的金属及合金，尤为重要（2）是某些工件或半成品能够成形的重要因素（3）可提高工件或构件在使用过程中的安全性。说明金属热加工对组织和性能的影响：消除铸态组织缺陷，提高力学性能；形成流线组织。钢材在热变形加工时为什么不出现硬化现象？：因为金属的热塑性加工时在再结晶温度以上的加工，在变形过程中产生的变形晶粒及加工硬化，由于同时进行着再结晶过程而被消除。 4、合金：由两种或两种以上的金属元素或金属元素与非金属元素组成的具有金属特性的物质；组元：组成合金最基本的独立物质；相：金属或合金中具有相同化学成分、相同结构并与其他部分由界面分开的均匀组成部分；组织：指用肉眼或显微镜所观察到的不同相或相的形状、分布及各相之间的组合状态。固溶体：溶质原子溶于溶剂晶格中而仍保持溶剂晶格类型的合金相；金属化合物：由化学性质差别大，原子直径大小不同的各元素组成的合金；匀晶转变：结晶时从液相结晶出单相固溶体的过程；包晶转变：在一定温度下，已结晶的一定成分的固相与剩余的一定成分的液相发生转变生成另一固相的过程。共晶转变：在一定温度下，由一定成分的液相同时结晶出成分一定的两个不同固相的过程；共析转变：在恒定温度下，一个特有成分的固相分解成另外两个与母成分不同的固相的转变。铁素体：碳溶解在a-Fe中形成的间隙固溶体；奥氏体：碳在r-Fe中形