外文翻譯--si3n4s45c的斷裂韌性界面裂紋

1、<p>　　Fracture Toughness of Si3N4/S45C Joint with an Interface Crack</p><p>　　Liedong Fu, Yukio Miyasita and Yoshiharu Mutoh</p><p>　　Copyright AD-TECH.; licensee AZoM.com Pty Ltd.</p>

2、;<p>　　This is an AZo Open Access Rewards System (AZo-OARS) article distributed under the terms of the AZo–OARS http://www.azom.com/oars.asp which permits unrestricted use provided the original work is p

3、roperly cited but is limited to non-commercial distribution and reproduction.</p><p>　　Posted: September 2005</p><p>　　Topics Covered</p><p><b>　　Abstract</b></p>

4、<p><b>　　Keywords</b></p><p>　　Introduction</p><p>　　Experimental</p><p>　　Specimen Preparation</p><p>　　Experimental Results</p><p>　　Os

5、cillatory Singular Stress Field of The Interface Crack and The Maximum Normal Stress Criteria</p><p>　　Elasto-Plastic Singular Stress Field at The Interface Crack Tip</p><p>　　Fem Analysis and E

6、valuation of Fracture Path and Toughness Based on the Elasto-Plastic Stress Intensity Factors</p><p>　　Conclusions</p><p>　　References</p><p>　　Contact Details</p><p>&

7、lt;b>　　Abstract</b></p><p>　　Fracture 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

8、4 mm has 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 Si3N4 from the crack tip in the direction of 40o&#

9、160;for cracks of 1 mm and 2 mm while it propagated along the interface for crack of 4 mm. Elasto-plastic analysis was carried out considerin</p><p><b>　　Keywords</b></p><p>　　I

10、nterface Crack, Fracture Toughness, Si3N4/S45C Joint, Thermal Residual Stress, Elasto-plastic Analysis</p><p>　　Introduction</p><p>　　The ceramic/metal joints have been increasingly applied in a

11、 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 m

12、etal and ceramic induces stress singularities at the interface edge.  Moreover, high thermal residual stress will be induced during the cooling process due to the mismatch of the thermal expansion coefficients.

13、  The stress si</p><p>　　The elastic solution of the singular stress field of the interface crack has been studied since 1959 [4-9].  Rice [10] has summarized the work in this field and s

14、et 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 joint bas

15、ed on the elastic theory.The plastic deformation of metal will inevitably appear near the crack tip due to the stress singularit</p><p>　　In this study, four point bending tests of Si3N4/S45C joint specimens

16、 with an interface crack were carried out.  Evaluation of the fracture path and fracture toughness was attempted based on the elasto-plastic analysis.</p><p>　　Experimental</p><p>　　Sp

17、ecimen Preparation</p><p>　　Figure 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 μm thickness was used

18、for the bonding between Si3N4 ceramics and S45C steel. Brazing was carried in a vacuum furnace (2.5x10-5 Torr).  The temperature of the furnace was increased at a rate of 20oC/min up to the brazi

19、ng temperature of 850oC and kept for 10 min, then decreased at a rate of 10oC/min.  The joining surfaces were polished with diamond powd</p><p>　　After brazing, an interface crack was introduced by

20、 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

21、 specimens had crack lengths of 1.0 mm and 2.0 mm.</p><p>　　Figure 1. Fracture toughness specimen.</p><p>　　Experimental Results</p><p>　　Four point bending tests were carried

22、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:</p><p>&l

23、t;b>　　(1)</b></p><p><b>　　with</b></p><p><b>　　(2)</b></p><p><b>　　(3)</b></p><p>　　Where Pf is the fracture load, a i

24、s the crack length, w the specimen width, t the specimen highness, L2 the outer span and L1 the inner span.</p><p>　　Table 1. Result of the fracture toughness tests.</p><p>　　As c

25、an be seen in Table 1, the specimens with a crack length of 4.0 mm indicate a higher fracture load than those with shorter crack lengths of 1.0 and 2.0 mm.  As the residual stress will redistribute after cuttin

26、g [2], the relaxation of thermal residual stress for longer crack length may be a possible reason.</p><p>　　Figure 2 shows the macroscopic observation of the fractured specimen.  For the specimens

27、with a crack length of 1.0 and 2.0 mm, crack propagated into Si3N4 directly 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

28、along the interface for about 1.0 mm and then kinked into Si3N4 in a direction of about 10o to the interface.</p><p>　　(a) a = 1.0mm</p><p>　　(b) a = 2.0mm</p><p>　　(c) a

29、= 4.0mm </p><p>　　(d) a = 4.0mm</p><p>　　Figure 2. Fractured specimens.</p><p>　　Oscillatory Singular Stress Field of The Interface Crack and The Maximum Normal Stress Criteria

30、</p><p>　　The elastic solution of the stress field of an interface crack has been accomplished by the Willims [4], Erdogan [5, 6], England [7] and Sih et al. [8, 9].  It has been found that the str

31、ess 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</p><p><b>　　

32、(4)</b></p><p>　　Here  is the bi-material constant that can be expressed as</p><p><b>　　(5)</b></p><p><b>　　(6)</b></p><p>　　whe

33、re µj and vj are the shear modulus and the Poisson’s ratio of the materials, respectively.</p><p>　　The stress intensity factors of the oscillatory singular stress field are defined as<

34、;/p><p><b>　　(7)</b></p><p>　　where, l is the reference length to eliminate the dimension of the oscillatory term.  Usually l takes the value of the whole

35、crack length, i.e. l=2a.</p><p>　　When the stress along the interface has been known, the stress intensity factors can be can be extrapolated as:</p><p><b>　　(8)</b></p><p

36、><b>　　(9)</b></p><p>　　Yuuki et al. [11, 12] have proposed up the maximum normal stress criteria for the fracture of interface crack.  Considering that the value of  is ver

37、y small, the normal stress can be approximately expressed as</p><p><b>　　(10)</b></p><p><b>　　where</b></p><p><b>　　(11)</b></p><p>

38、　　W1= e-ε(π-θ), W2= eε(π+θ)                (12)</p><p><b>　　(13)</b></p><p>　　The direction of the max

39、imum normal stress can be determined from:</p><p>　　?B(θ,ε,y)/? θ = 0           (14)</p><p>　　Let θ0 represent the direction of the ma

40、ximum normal stress, the corresponding stress intensity factor can be expressed as:</p><p><b>　　(15)</b></p><p>　　Fracture will occur along the direction of θ0 when Kθmax&#

41、160;reaches the KIC value of the base material.  It should be noted that fracture may occur along the interface when θ0 becomes smaller than certain value, since the strength of interface is usua

42、lly lower than that of the base material.</p><p>　　Elasto-Plastic Singular Stress Field at The Interface Crack Tip</p><p>　　The elasto-plastic singular stress field for a linear hardening materi

43、al [13] has been found to be substantially the same as that of elastic material whose elastic constants are defined as:</p><p><b>　　(16)</b></p><p>　　where E is the Young’s modulus a

44、nd H’ the hardening coefficient.</p><p>　　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

45、tip.  The governing region of the elasto-plastic singular stress field will be confined in a small region around the crack tip inside the yield zone.  For ceramic/metal joint, considering that the val

46、ue of hardening coefficient is much less than the value of Young’s modulus, it can be found from Eq. (16) and Eq. (5) that</p><p><b>　　(17)</b></p><p>　　FEM Analysis and Evaluation o

47、f Fracture Path and Toughness Based on the Elasto-Plastic Stress Intensity Factors</p><p>　　FEM analysis was carried out under plane stress condition using the program of ABAQUS.  Si3N4 is ass

48、umed as an elastic material whose material constants are independent of temperature and E=289 GPa, v=0.25 and CTE=4.2x10-6.  S45C steel is assumed as a linear hardening material with the material constants

49、 listed in Table 2 [14].  The stress free temperature is considered to be 550oC for the analysis of the thermal residual stress.</p><p>　　Table 2. Material constants of S45C</p><p&g

50、t;　　For comparison, the elastic analysis was also carried out.  Calculated from the elastic constants of 25oC, the bi-material constantfor elastic case is 0.01588.  Table 3 lists the stress intensity

51、factors as well as the direction of the maximum normal stress obtained by the elastic analysis.  It can be found that the  value due to residual stress is much higher than  and the values of

52、 θ0 due to the residual stress are almost the same, which are about 70o.  The specimen with a crack length of 2.0 </p><p>　　Table 3. Stress intensity factors and the direction of the maxi

53、mum normal stress according to the elastic analysis.</p><p>　　However, the results of elastic analysis apparently contradict with that the value of Kθmax is much higher than KIC value of Si3N4

54、, which is about 6.0 MPa√m [15].  Also, the elastic analysis cannot explain why the specimen with a=4.0 mm indicates higher fracture load than the specimen with a=1.0 mm since Kθmax due to the residual str

55、ess for a=4.0 mm is larger than that for a=1.0 mm.</p><p>　　Figures 3 and 4 show the stress distribution the interface obtained by the elasto-plastic analysis.  A line with the slop of –0.5 is also

56、 plotted in the figures for reference.  We can see that the curves are almost parallel to the reference line in the region r<10-6m, which indicates that the stress near the crack tip is dominated by the elas

57、to-plastic singular stress field.</p><p>　　Figure 3. Normal stress distribution along the interface.</p><p>　　Figure 4. Shear stress distribution along the interface.</p><p&

58、gt;　　Figures 5 and 6 show the uncoupled components defined by Eq. (8) and Eq. (9).  Different from the elastic case, here the reference length l takes thevalue of 1.0-6 m, which is close to the s

59、ize of governing region of the elasto-plastic singular stress field.  Figure 5 shows stress distribution due to residual stress and Figure 6 shows the stress distribution due to residual stress and applied load

60、.  It can be found that the curves are almost parallel to reference line in the region r<1.0-5 m.</p><p>　　Figure 5. Distribution of the decoupled components along the interface for th

61、e residual stress. </p><p>　　Figure 6. Distribution of the decoupled components along the interface at the fracture of specimen.</p><p>　　Table 4 lists the stress intensity factors and the

62、directions of maximum normal stress obtained by the elasto-plastic analysis.  It can be found that Kθmax due to residual stress decreases in the sequence of a=2.0 mm, a=1.0 mm and a=4.0 mm.  

63、;This result can explain why the specimen with a crack length of 4.0 mm indicates higher fracture load compared to the other specimens.  The applied load tends to decrease the value of K2.  The decrea

64、se of K2 for a=4.0 mm is especially obvious and the value o</p><p>　　Table 4. Stress intensity factors and the direction of the maximum normal stress according to the elasto-plastic analysis.</p

65、><p>　　Conclusions</p><p>　　Fracture toughness tests were carried out on Si3N4/S45C joint specimens with interface cracks of different lengths. Evaluation of fracture path and fracture toughness wa

66、s carried out based on elasto-plastic analysis in which S45C steel was assumed as a linear hardening material.  The conclusions obtained can be summarized as:</p><p>　　?    

67、0;    The thermal residual stress has a significant effect on the fracture toughness of the joint.  Due to the effect of residual stress, the specimen with a crack length of 4.0 mm has highe

68、r fracture toughness than those with crack lengths of 1.0 mm and 2.0 mm.  A crack propagated into Si3N4directly from the initial crack tip in the direction of 40o for crack lengths of 1.0 mm or 2.0 mm, whi

69、le it propagated along the interface for the crack length of 4.0 mm.</p><p>　　?         Stress near the crack tip is dominated by the elasto-plastic singular stre

70、ss field.  Maximum σθ criterion based on the elasto-plastic singular stress field could be successfully applied for evaluating the fracture path and fracture toughness value. 3. Kθmax value

71、due to the residual stress decreases in the sequence of a=2.0 mm, a=1.0 mm and a=4.0 mm.  This is the same sequence of fracture load of the specimens with a=2.0 mm, a=1.0 mm and a=4.0 mm.  The applied

72、 stress resulted in a decr</p><p>　　References</p><p>　　1.       H. Kobayashi, Y. Arai, H. Nakamura and T. Sato, “Strength Evaluation of Ceramic-Metal Joints”,

73、 Materials Science and Engineering, A143 (1991) 91-102.</p><p>　　2.       H. Kobayashi, H., Nakamura, A. Todoroki, W. Park, T. Koide and H. Taniai, Effect of specimen cut o

74、ff and size on bending strength of ceramic/metal joints, Trans. of JSME, A60-569 (1994) 65-70.</p><p>　　3.       J.H. Qiu, S. Nakamura, M. Kawagoe and M. Morita, “Influence

75、 of Joining Strength of Si3N4/S45C on Residual Stress”, Journal of Inorganic Materials, 13-4 (1998) 167-172.</p><p>　　4.       M.L. Williams, “The Stress Around a Fault or

76、Crack in Dissimilar Media”, Bulletin of the Seismological Society of America, 49-2 (1959) 199-204.</p><p>　　5.       F. Erdogan, “Stress Distribution in Bonded Dissimilar M

77、aterials with Cracks”, J. Appl. Mech., 32 (1965) 403-411.</p><p>　　6.       F. Erdogan, “Stress Distribution in Bonded Dissimilar Materials Containing Circular Ring-shaped

78、Cavities”, J.Appl.Mech., 32 (1965) 829-836.</p><p>　　7.       A. H. England, “A Crack between Dissimilar Medias”, J. Appl. Mech., 32 (1965) 400-407.</p><p>　　8

79、.       G..C. Sih and J. R. Rice, “The Bending of Plates of Dissimilar Materials with Cracks”, J. Appl. Mech., 31 (1964) 477-483.</p><p>　　9.     &

80、#160; J. R. Rice and G.C. Sih, “Plane Problems of Cracks in Dissimilar Media”, J. Appl. Mech., 32 (1965) 418-423.</p><p>　　10.   J. R. Rice, “Elastic Fracture Mechanics Concepts for Inter

81、facial Cracks”, J. Appl. Mech., 55 (1988) 98-103.</p><p>　　11.   R. Yuuki and J.Q. Xu, Eng. Fract. Mech., “Stress Based Criterion for an Interface crack Kinking out of the Interface in Dissimi

82、lar Materials”, 41-5 (1992) 635-644.</p><p>　　12.   R. Yuuki, J.Q. Xu and Y. Mutoh, “Evaluation of Fracture and Strength of Metal/Ceramic bonded Joints Based on Interfacial Fracture Mechanics”

83、, Trans. of JSME, A60-569 (1994) 37-45.</p><p>　　13.   J.Q. Xu and L. Fu, “Stress Field near an Interface Edge of Linear Hardening Materials”,Journal of Zhejiang University: Science V No.3-1 (

84、2002) 13-18.</p><p>　　14.   N. Okabe, M. Takahashi, X. Zhu, K. Kagawa and M. Maruyama, “Residual Stress and Fatigue Strength Properties of Ceramic/Metal joints”, J. Soc. Mat. Sci., Japan, 48-1

85、2 (1999) 1416-1422.</p><p>　　15.   Y. Mutoh and I. Yumoto, “Fracture Toughness Evaluation for Ceramics/Metal Joints”, Trans. of the Symposium of Material Mechanics of JSME, No.900-50 (1990) 18

86、5-190.</p><p>　　Si3N4/S45C的斷裂韌性界面裂紋</p><p>　　Liedong富，鳩山由紀(jì)夫Miyasita和吉春Mutoh</p><p><b>　　題目</b></p><p><b>　　摘要</b></p><p><b>　

87、　關(guān)鍵詞</b></p><p><b>　　導(dǎo)言</b></p><p><b>　　實(shí)驗(yàn)</b></p><p><b>　　樣品制備</b></p><p><b>　　實(shí)驗(yàn)結(jié)果</b></p><p>　　振蕩奇

88、異應(yīng)力場(chǎng)的界面裂紋和最大正應(yīng)力準(zhǔn)則</p><p>　　彈塑性應(yīng)力場(chǎng)奇異界面裂紋尖端</p><p>　　有限元分析與評(píng)價(jià)路徑和斷裂韌性基于彈塑性應(yīng)力強(qiáng)度因子</p><p><b>　　結(jié)論</b></p><p><b>　　參考文獻(xiàn)</b></p><p><b&

89、gt;　　聯(lián)系方式</b></p><p><b>　　摘要</b></p><p>　　斷裂韌性試驗(yàn)，進(jìn)行了Si3N4/S45C標(biāo)本界面裂紋的長(zhǎng)度不同。   結(jié)果發(fā)現(xiàn)，試樣的裂紋的4毫米具有較高的斷裂韌性明顯高于裂縫的1毫米和2毫米由于減少殘余應(yīng)力。   骨折繁殖到第3硅ñ 

90、4裂紋尖端的方向40 °的裂縫1毫米和2毫米，而它繁殖沿界面裂紋的4毫米。   彈塑性分析進(jìn)行了審議S45C的線(xiàn)性硬化材料和Si 3 ñ 4彈性材料。   結(jié)果發(fā)現(xiàn)，周?chē)膽?yīng)力裂紋尖端主要是由彈塑性奇異應(yīng)力場(chǎng)，這是大致相同的彈性應(yīng)力場(chǎng)奇異的界面裂紋。   評(píng)價(jià)斷裂韌性和道路進(jìn)行了基于應(yīng)力強(qiáng)

91、度因子的彈塑性奇異應(yīng)力場(chǎng)。</p><p><b>　　關(guān)鍵詞</b></p><p>　　界面裂紋，斷裂韌性，熱殘余應(yīng)力，彈塑性分析</p><p><b>　　導(dǎo)言</b></p><p>　　陶瓷與金屬的聯(lián)合已越來(lái)越多地應(yīng)用在廣泛的工程領(lǐng)域，因?yàn)樘沾删哂蟹€(wěn)定的力學(xué)性能在高溫下和良好的抗磨損，侵

92、蝕和氧化。 然而，不同的材料性能之間的金屬，陶瓷誘導(dǎo)應(yīng)力奇異界面優(yōu)勢(shì)。 此外，較高的熱殘余應(yīng)力會(huì)引起在冷卻過(guò)程由于不匹配的熱膨脹系數(shù)。應(yīng)力一道奇異的熱殘余應(yīng)力降低強(qiáng)度的陶瓷與金屬的聯(lián)合，使評(píng)價(jià)兵力困難。許多工程已完成的殘余應(yīng)力和強(qiáng)度評(píng)價(jià)陶瓷與金屬接頭。舉例來(lái)說(shuō)，小林等人。調(diào)查的抗彎強(qiáng)度和殘余應(yīng)力的Si3N4/S45C聯(lián)合和影響大小的標(biāo)本的抗彎強(qiáng)度。調(diào)查的影響，殘余應(yīng)力和循環(huán)荷載強(qiáng)度的Si3N4/S45C聯(lián)合。但是，由

93、于問(wèn)題的復(fù)雜性，普遍評(píng)價(jià)方法的陶瓷/金屬聯(lián)合尚未提出。彈性解決奇異應(yīng)力場(chǎng)的界面裂紋，研究了自1959年以來(lái)， 賴(lài)斯總結(jié)了在這一領(lǐng)域的工作，并建立彈性斷裂力學(xué)的概念，界面裂縫。 佑輝等人提出了最高標(biāo)準(zhǔn)的正常應(yīng)力性骨折的預(yù)測(cè)路徑和強(qiáng)度的陶瓷與金屬的聯(lián)合為基礎(chǔ)的彈性理論。 塑性變形的金屬將不可避免地出現(xiàn)附近的裂紋尖端由于應(yīng)力奇異。對(duì)于大多數(shù)陶瓷與金屬接頭的塑性變形金屬有重大影響的力量，陶瓷與金屬聯(lián)合。由于復(fù)雜的分

94、析，評(píng)價(jià)骨折的路徑和強(qiáng)度的陶瓷/金屬的聯(lián)合為基礎(chǔ)的彈塑性理論尚未作出</p><p><b>　　實(shí)驗(yàn) 標(biāo)本 制備</b></p><p><b>　　圖1</b></p><p>　　圖1顯示了幾何形狀和尺寸的標(biāo)本。   基于銀釬焊合金（銀， 71 ％ ，銅， 27 ％ ，鈦， 2

95、 ％ ）與60微米的厚度用于粘接硅之間的陶瓷和S45C鋼。   釬焊是在真空爐（ 2.5x10 -5子） 。   的溫度爐提高率為20 攝氏度 /分鐘到釬焊溫度為850 攝氏度 ，并保持10分鐘，然后在一個(gè)下降率為10 攝氏度 /分鐘。   加入表面拋光鉆石粉直徑0.25微米。&

96、#160;  在釬焊，一個(gè)接觸壓力0.002兆帕適用。</p><p>　　釬焊后，一個(gè)界面裂紋介紹了放電的方法切割線(xiàn)的直徑0.1毫米。 四標(biāo)本不同裂紋長(zhǎng)度準(zhǔn)備。兩個(gè)標(biāo)本了裂紋長(zhǎng)度為4.0毫米，而其他兩個(gè)標(biāo)本了裂紋長(zhǎng)度為1.0毫米和2.0毫米。</p><p><b>　　實(shí)驗(yàn)結(jié)果</b></p><p>　　四點(diǎn)

97、彎曲試驗(yàn)進(jìn)行了斷裂韌性標(biāo)本在十字頭速度為0.5毫米/分鐘。   表1顯示的結(jié)果，斷裂韌性。   </p><p>　　表觀(guān)斷裂韌性的定義為：</p><p>　　其中p f是斷裂負(fù)荷，一個(gè)是裂紋長(zhǎng)度，瓦特試樣寬度，噸試樣高度，L2 外跨度和L 1 ，內(nèi)跨度。</p><p>　

98、　表1 。 結(jié)果斷裂韌性試驗(yàn)。</p><p>　　可以看出，在表1 ，標(biāo)本與裂紋長(zhǎng)度的四點(diǎn)○毫米表明較高的斷裂載荷比那些短的裂紋長(zhǎng)度的1.0和2.0毫米。 由于殘余應(yīng)力重新分配后，將削減放寬對(duì)熱殘余應(yīng)力的長(zhǎng)期裂紋長(zhǎng)度可能是一個(gè)可能的原因。圖2顯示了宏觀(guān)觀(guān)測(cè)裂縫標(biāo)本。裂縫延續(xù)到標(biāo)本的裂紋長(zhǎng)度的1.0和2.0毫米，硅直接從第四處初始裂紋尖端的方向約40°。對(duì)于標(biāo)本的裂紋長(zhǎng)度為4.0毫米

99、，沿裂紋傳播的接口約1.0毫米，然后扭折到四個(gè)方向約10°接口。</p><p>　　(a) a = 1.0mm</p><p>　　(b) a = 2.0mm</p><p>　　(c) a = 4.0mm</p><p>　　(d) a = 4.0mm</p><p>　　振蕩奇異應(yīng)力場(chǎng)的位界面裂紋和最大

100、正應(yīng)力準(zhǔn)則</p><p>　　Willims ，埃爾多安，英格蘭等，已經(jīng)完成了彈性的解決方案的應(yīng)力場(chǎng)的界面裂紋分析。人們發(fā)現(xiàn)，應(yīng)力場(chǎng)附近的界面裂紋尖端的裂紋樣子奇特。根據(jù)極坐標(biāo)位于裂紋尖端的應(yīng)力場(chǎng)可表示為</p><p>　　這里 是材料常數(shù)，可表示為</p><p>　　而μ j 和 V j的剪切模量和泊松比的

101、材料，分別。</p><p>　　應(yīng)力強(qiáng)度因子的應(yīng)力場(chǎng)被界定為</p><p>　　在那里， l是長(zhǎng)度的參考，以消除層面的振蕩任期。   1-5 升的價(jià)值需要對(duì)整個(gè)裂紋長(zhǎng)度，即升= 2A型。</p><p>　　當(dāng)應(yīng)力沿界面已眾所周知，應(yīng)力強(qiáng)度因子可以可以推斷為：</p><p>　　佑輝等人

102、提出了最大正應(yīng)力準(zhǔn)則骨折的界面裂紋?？紤]到非常小，正常的壓力大約可以表示為</p><p>　　W1= e-ε(π-θ), W2= eε(π+θ)     </p><p>　　該方向的最大正應(yīng)力可確定：</p><p>　　?B(θ,ε,y)/? θ = 0     

103、;     </p><p>　　讓?duì)?#160;0代表方向的最大正應(yīng)力，相應(yīng)的應(yīng)力強(qiáng)度因子可以表示為：         </p><p>　　骨折將發(fā)生方向的 θ 0 當(dāng)k θmax 達(dá)到的KIC的基

104、礎(chǔ)材料。   應(yīng)該指出的是，可能會(huì)發(fā)生斷裂沿界面 θ 0 時(shí) 變得小于一定的價(jià)值，因?yàn)閺?qiáng)度的界面通常是低于基礎(chǔ)材料。</p><p>　　彈塑性應(yīng)力場(chǎng)奇異界面裂紋尖端</p><p>　　彈塑性奇異應(yīng)力場(chǎng)的線(xiàn)性硬化材料已被發(fā)現(xiàn)基本上相同的彈性材料的彈性常數(shù)的定義是：    

105、0;    </p><p>　　其中E是楊氏模量和H '硬化系數(shù)。</p><p>　　因此，彈塑性應(yīng)力場(chǎng)奇異的界面裂紋尖端是大致相同的彈性應(yīng)力場(chǎng)奇異的界面裂紋尖端。 管轄區(qū)域的彈塑性奇異應(yīng)力場(chǎng)將限于在一個(gè)小附近地區(qū)的內(nèi)裂紋尖端區(qū)的產(chǎn)量。 陶瓷與金屬聯(lián)合，考慮到價(jià)值的硬化系數(shù)是遠(yuǎn)遠(yuǎn)低于價(jià)值的楊氏模量，可以發(fā)現(xiàn) 

106、     </p><p>　　有限元分析法和評(píng)價(jià)路徑和斷裂韌性基于彈塑性應(yīng)力強(qiáng)度因子</p><p>　　有限元分析是進(jìn)行平面應(yīng)力條件下使用的程序。 彈性材料，其材料常數(shù)是完全獨(dú)立的溫度E = 289千兆，W= 0.25和熱膨脹系數(shù)= 4.2x10 -6 。   S45C鋼承擔(dān)作

107、為一個(gè)線(xiàn)性硬化材料與材料常數(shù)列于表2 [ 14 ] 。   免費(fèi)的溫度應(yīng)力被認(rèn)為是550° ，用于分析的熱殘余應(yīng)力。</p><p>　　表2 。 材料常數(shù)S45C</p><p>　　作為比較，彈性分析還開(kāi)展。   計(jì)算出的彈性常數(shù)25 攝氏度 ，雙向材料常數(shù) 彈性是0

108、.01588案件。   表3列出的應(yīng)力強(qiáng)度因子，以及方向的最大正應(yīng)力得到了彈性分析。它可發(fā)現(xiàn)，價(jià)值由于殘余應(yīng)力遠(yuǎn)遠(yuǎn)高于   和價(jià)值觀(guān)θ0由于殘余應(yīng)力幾乎是相同的，這是約70o試樣的裂紋長(zhǎng)度的2.0毫米的最高值的K θmax由于殘余應(yīng)力。K θmax由于疊加的殘余應(yīng)力和應(yīng)用應(yīng)力斷裂韌性測(cè)試已接近那些由于殘余應(yīng)力。</p><p>　　表

109、3 。 應(yīng)力強(qiáng)度因子和方向的最大正應(yīng)力按照彈性分析。</p><p>　　然而，結(jié)果顯然彈性分析矛盾與價(jià)值的K θmax遠(yuǎn)遠(yuǎn)高于K 集成電路價(jià)值的硅三語(yǔ)4 ，大約是6.0 Mpa/m。   此外，彈性分析不能解釋為什么標(biāo)本與= 4.0毫米表明較高的斷裂載荷比試樣與a=1.0毫米自K θmax由于殘余應(yīng)力為= 4.0毫米，大于一個(gè)= 1.0毫米。

110、圖3</p><p><b>　　圖4</b></p><p>　　圖3和圖4表明，應(yīng)力分布的界面獲得的彈塑性分析。曲線(xiàn)上的-0.5也是推測(cè)的數(shù)字，以供參考。我們可以看到，曲線(xiàn)幾乎平行的參考線(xiàn)在該地區(qū)r < 10-6米，這表明，附近的應(yīng)力裂紋尖端占主導(dǎo)地位的是彈塑性奇異應(yīng)力場(chǎng)。圖5圖6</p><p>　　圖5和圖6顯示解耦組件

111、定義的方程。不同的彈性情況下，這里的參考長(zhǎng)度 L需要的價(jià)值1.0 -6米，接近大小的規(guī)劃的彈塑性奇異應(yīng)力場(chǎng)。 圖5顯示應(yīng)力分布由于殘余應(yīng)力和圖6顯示的應(yīng)力分布由于殘余應(yīng)力和應(yīng)用負(fù)載。它可以發(fā)現(xiàn)，曲線(xiàn)幾乎平行的參考線(xiàn)在該地區(qū)r = 1.0 -5米。表4列出了應(yīng)力強(qiáng)度因子和方向的最大正應(yīng)力得到了彈塑性分析?？梢园l(fā)現(xiàn)K θmax 由于殘余應(yīng)力下降的順序a= 2.0毫米，a=1.0毫米

112、，a= 4.0毫米。這一結(jié)果可以解釋為什么試樣的裂紋長(zhǎng)度的4.0毫米表明較高的斷裂載荷相比，其他標(biāo)本。應(yīng)用負(fù)荷趨于減少的價(jià)值的K 2 。減少的K 2 ， a= 4.0 mm是尤為明顯的價(jià)值θ 0為= 4.0毫米，這是遠(yuǎn)遠(yuǎn)小于一個(gè)a= 1.0毫米，a= 2.0毫米。 這同意的實(shí)驗(yàn)結(jié)果，那里的標(biāo)本與= 1.0毫米，a = 2.0毫米的裂縫角度約40°的接口，而標(biāo)本的=四點(diǎn)零毫米裂縫

113、沿界面。值的K θmax 由于殘余應(yīng)力，這是發(fā)生骨折時(shí)，幾乎是相同的，不論裂紋的長(zhǎng)度。 KIC 等值的Si3N4，雖然低于它。小林等人[ 1 ]發(fā)現(xiàn)在彎曲試驗(yàn)的Si3N4/S45C聯(lián)合的結(jié)果可分為兩個(gè)群體，其中顯示了相</p><p>　　表4 。 應(yīng)力強(qiáng)度因子和方向的最大正應(yīng)力根據(jù)彈塑性分析。</p><p><b>　　結(jié)論</b

114、></p><p>　　斷裂韌性試驗(yàn)進(jìn)行了四Si3N4/S45C聯(lián)合標(biāo)本界面裂紋的長(zhǎng)度不同。評(píng)價(jià)斷裂的路線(xiàn)和斷裂韌性進(jìn)行了基于彈塑性分析中Si3N4鋼承擔(dān)作為一個(gè)線(xiàn)性硬化材料。 所得結(jié)論可以概括為：   熱殘余應(yīng)力有重大影響的斷裂韌性的聯(lián)合。由于影響的殘余應(yīng)力，試樣的裂紋長(zhǎng)度的4.0毫米具有較高的斷裂韌性比那些裂紋長(zhǎng)度為1.0毫米和2.0毫米。裂紋傳播Si3N4/S4

115、5C直接從最初的裂紋尖端的方向40°的裂紋長(zhǎng)度為1.0毫米或2.0毫米，而它繁殖沿界面裂紋長(zhǎng)度為4.0毫米。 不久應(yīng)力裂紋尖端占主導(dǎo)地位的是彈塑性奇異應(yīng)力場(chǎng)。  最大 σ θ 標(biāo)準(zhǔn)為基礎(chǔ)的彈塑性應(yīng)力場(chǎng)奇異可以成功地用于評(píng)估骨折的道路和斷裂韌性值。 Kθmax 價(jià)值由于殘余應(yīng)力下降的順序a= 2.0毫米，a=1.0毫米，a = 4.0毫米。