百度文库 - 让每个人平等地提升自我
Fracture Toughness of Si3N4/S45C Joint with an Interface Crack
Liedong Fu, Yukio Miyasita and Yoshiharu Mutoh
Copyright AD-TECH.; licensee Pty Ltd.
This is an AZo Open Access Rewards System (AZo-OARS) article distributed under the terms of the AZo–OARS which permits unrestricted use provided the original work is properly cited but is limited to non-commercial distribution and reproduction. Posted: September 2005
Topics Covered
Abstract
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 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 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 considering S45C as the linear hardening material and Si3N4 as 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. Evaluation of the fracture path and toughness was carried out based on the stress intensity factors of the elasto-plastic singular stress field. Keywords
Interface Crack, Fracture Toughness, Si3N4/S45C Joint, Thermal Residual Stress, Elasto-plastic Analysis Introduction
The ceramic/metal joints have been 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 interface edge. Moreover, high thermal residual stress will be induced during the cooling process due to the mismatch of the thermal expansion
1
百度文库 - 让每个人平等地提升自我
coefficients. The stress singularity together with the thermal residual stress degrades the strength of ceramic/metal joint and makes the evaluation of the strength 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 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 the 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 joint 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, 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 attempted based on the elasto-plastic analysis. Experimental
Specimen Preparation
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 for the bonding between Si3N4 ceramics and S45C steel. Brazing 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 μm diameter. During the brazing, a 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 crack lengths of 1.0 mm and 2.0 mm.
2
百度文库 - 让每个人平等地提升自我
Figure 1. Fracture toughness specimen. Experimental Results
Four 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:
(1)
with
(2)
(3)
Where Pf is the fracture load, a is the crack length, w the specimen width, t the specimen highness, L2 the outer span and L1 the inner span.
Table 1. Result of the fracture toughness tests.
No. 1 2 3 4 Crack length a (mm) Pf (N) σ f (MPa) FI KIApparent(MPa√m) As can 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 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 of the fractured specimen. For the specimens with a crack length of 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 along the interface for about 1.0 mm and then kinked into Si3N4 in a direction of about 10o to the interface.
3
百度文库 - 让每个人平等地提升自我
(a) a = 1.0mm
(b) a = 2.0mm
(c) a = 4.0mm
(d) a = 4.0mm
Figure 2. Fractured specimens.
Oscillatory Singular Stress Field of The Interface Crack and The Maximum Normal Stress Criteria
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 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)
Here is the bi-material constant that can be expressed as
(5)
(6)
where μj and vj are the shear modulus and the Poisson’s ratio of the materials, respectively.
The stress intensity factors of the oscillatory singular stress field are defined as
(7)
4
百度文库 - 让每个人平等地提升自我
where, l is the reference length to eliminate the dimension of the oscillatory term. Usually l takes 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 that the value of is very small, the normal stress can be approximately expressed as
(10)
where
(11)
W1= e-ε(π-θ), W2= eε(π+θ) (12)
(13)
The direction of the maximum normal stress can be determined from:
?B(θ,ε,y)/? θ = 0 (14)
Let θ0 represent the direction of the maximum normal stress, the corresponding stress intensity factor can be expressed as:
(15)
Fracture will occur along the direction of θ0 when Kθmax 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 usually lower than that of the base material.
5
中文翻译材料
