中文翻译材料.docx

1、中文翻译材料Fracture Toughness of Si3N4/S45C Joint with an Interface CrackLiedong Fu, Yukio Miyasita and Yoshiharu MutohCopyright AD-TECH.; licensee Pty Ltd.This is an AZo Open Access Rewards System (AZo-OARS) article distributed under the terms of the AZoOARSwhich permits unrestricted use provided the or

2、iginal work is properly cited but is limited to non-commercial distribution and reproduction.Posted: September 2005Topics CoveredAbstractFracture toughness tests were carried out for Si3N4/S45C specimens with interface cracks of different lengths.It was found that the specimen with a crack of 4 mm h

3、as higher apparent fracture toughness than those with cracks of 1 mm and 2 mm due to the reduction of the residual stress.Fracture propagated into Si3N4from the crack tip in the direction of 40ofor cracks of 1 mm and 2 mm while it propagated along the interface for crack of 4 mm.Elasto-plastic analy

4、sis was carried out considering S45C as the linear hardening material and Si3N4as the elastic material.It was found that the stress around the crack tip is dominated by an elasto-plastic singular stress field, which is substantially the same as the elastic singular stress field of an interface crack

5、.Evaluation of the fracture path and toughness was carried out based on the stress intensity factors of the elasto-plastic singular stress field.KeywordsInterface Crack, Fracture Toughness, Si3N4/S45C Joint, Thermal Residual Stress, Elasto-plastic AnalysisIntroductionThe ceramic/metal joints have be

6、en increasingly applied in a wide range of engineering fields because the ceramic has stable mechanical properties at high temperature and good resistance to wear, erosion and oxidation.However, the difference of material properties between metal and ceramic induces stress singularities at the inter

7、face edge.Moreover, high thermal residual stress will be induced during the cooling process due to the mismatch of the thermal expansion coefficients.The stress singularity together with the thermal residual stress degrades the strength of ceramic/metal joint and makes the evaluation of the strength

8、 difficult.Many works have been done about the residual stress and the strength evaluation of ceramic/metal joints.For example, Kobayashi et al. 1, 2 have investigated the bending strength and residual stress of Si3N4/S45C joint and the effect of the size of the specimen on the bending strength.Qiu

9、et al. 3 have investigated the influence of residual stress and cyclic load on the strength of Si3N4/S45C joint.However, due to the complexity of the problem, a generalized evaluation method for the ceramic/metal joint has not yet been proposed.The elastic solution of the singular stress field of th

10、e interface crack has been studied since 1959 4-9.Rice 10 has summarized the work in this field and set up the elastic fracture mechanics concepts for interfacial cracks.Yuuki et al. 11, 12 have proposed the maximum normal stress criteria for predicting fracture path and strength of ceramic/metal jo

11、int based on the elastic plastic deformation of metal will inevitably appear near the crack tip due to the stress singularity.For most of the ceramic/metal joints, the plastic deformation of metal has a significant influence on the strength of the ceramic/metal joint.Due to the analytical complexity

12、, the evaluation of the fracture path and strength of ceramic/metal joint based on the elasto-plastic theory has not yet been made.In this study, four point bending tests of Si3N4/S45C joint specimens with an interface crack were carried out.Evaluation of the fracture path and fracture toughness was

13、 attempted based on the elasto-plastic analysis.ExperimentalSpecimenPreparationFigure 1 shows the geometry and dimensions of Si3N4/S45C joint specimen.The silver based brazing alloy (wt% is: Ag, 71%, Cu, 27%, Ti, 2%) with 60 m thickness was used for the bonding between Si3N4ceramics and S45C steel.B

14、razing was carried in a vacuum furnace Torr).The temperature of the furnace was increased at a rate of 20oC/min up to the brazing temperature of 850oC and kept for 10 min, then decreased at a rate of 10oC/min.The joining surfaces were polished with diamond powder of m diameter.During the brazing, a

15、contact pressure of MPa was applied.After brazing, an interface crack was introduced by the electric discharge method with the cutting wire of 0.1 mm diameter.Four specimens with different crack lengths were prepared.Two of the specimens had crack lengths of 4.0 mm and the other two specimens had cr

16、ack lengths of 1.0 mm and 2.0 mm.Figure 1.Fracture toughness specimen.Experimental ResultsFour point bending tests were carried out on the fracture toughness specimens at a crosshead speed of 0.5 mm/min.Table 1 shows the results of the fracture toughness.The apparent fracture toughness is defined as

17、:(1)with(2)(3)Where Pfis the fracture load, a is the crack length, w the specimen width, t the specimen highness, L2the outer span and L1the inner span.Table 1.Result of the fracture toughness tests.No.Crack length a (mm)Pf(N)f(MPa)FIKIApparent(MPam)1234As can be seen in Table 1, the specimens with

18、a crack length of 4.0 mm indicate a higher fracture load than those with shorter crack lengths of and 2.0 mm.As the residual stress will redistribute after cutting 2, the relaxation of thermal residual stress for longer crack length may be a possible reason.Figure 2 shows the macroscopic observation

19、 of the fractured specimen.For the specimens with a crack length of and 2.0 mm, crack propagated into Si3N4directly from the initial crack tip in the direction of about 40o.For the specimens with a crack length of 4.0 mm, the crack propagated along the interface for about 1.0 mm and then kinked into

20、 Si3N4in a direction of about 10oto the interface.(a) a = 1.0mm(b) a = 2.0mm(c) a = 4.0mm (d) a = 4.0mmFigure 2.Fractured specimens.Oscillatory Singular Stress Field of The Interface Crack and The Maximum Normal Stress CriteriaThe elastic solution of the stress field of an interface crack has been a

21、ccomplished by the Willims 4, Erdogan 5, 6, England 7 and Sih et al. 8, 9.It has been found that the stress field near the interface crack tip has the oscillatory singularity.Under the polar coordinate with the origin located at the crack tip, the stress field can be expressed as(4)Hereis the bi-mat

22、erial constant that can be expressed as(5)(6)where jandvjare the shear modulus and the Poissons ratio of the materials, respectively.The stress intensity factors of the oscillatory singular stress field are defined as(7)where,lis the reference length to eliminate the dimension of the oscillatory ter

23、m.Usuallyltakes the value of the whole crack length, . l=2a.When the stress along the interface has been known, the stress intensity factors can be can be extrapolated as:(8)(9)Yuuki et al. 11, 12 have proposed up the maximum normal stress criteria for the fracture of interface crack.Considering tha

24、t the value ofis very small, the normal stress can be approximately expressed as(10)where(11)W1= e-(-), W2= e(+)(12)(13)The direction of the maximum normal stress can be determined from:B(,y)/ = 0(14)Let 0represent the direction of the maximum normal stress, the corresponding stress intensity factor

25、 can be expressed as:(15)Fracture will occur along the direction of0when Kmaxreaches the KICvalue of the base material.It should be noted that fracture may occur along the interface when0becomes smaller than certain value, since the strength of interface is usually lower than that of the base materi

26、al.Elasto-Plastic Singular Stress Field at The Interface Crack TipThe elasto-plastic singular stress field for a linear hardening material 13 has been found to be substantially the same as that of elastic material whose elastic constants are defined as:(16)where E is the Youngs modulus and H the har

27、dening coefficient.Therefore, the elasto-plastic singular stress field at the interface crack tip is substantially the same as the elastic singular stress field of the interface crack tip.The governing region of the elasto-plastic singular stress field will be confined in a small region around the c

28、rack tip inside the yield zone.For ceramic/metal joint, considering that the value of hardening coefficient is much less than the value of Youngs modulus, it can be found from Eq. (16) and Eq. (5) that(17)FEM Analysis and Evaluation of Fracture Path and Toughness Based on the Elasto-Plastic Stress I

29、ntensity FactorsFEM analysis was carried out under plane stress condition using the program of ABAQUS.Si3N4is assumed as an elastic material whose material constants are independent of temperature and E=289 GPa,v= and CTE=.S45C steel is assumed as a linear hardening material with the material consta

30、nts listed in Table 2 14.The stress free temperature is considered to be 550oC for the analysis of the thermal residual stress.Table 2.Material constants of S45C25oC100oC200oC300oC400oC500oC600oCE(GPa)206206201197192187183vY-(MPa)375348333309280241193H (MPa)138120562680232516851026687CTE (10-6)For comparison, the elastic analysis was also carried out.Calculated from the elastic constants of 25oC, the bi-material constantfor elastic case is .Table 3 lists the stress intensity factors as well as the direct