outer layers near the surface increase strength, flaw tol- 2. Thermal residual stresses erance, fatigue strength, fracture toughness and stress and its calculation corrosion cracking. In the case of symmetrical lami- In this work the two-component brittle layered com- nates, this can be done by choosing the layer compo- posites with symmetric macrostructure are considered sitions such that the coefficient of thermal expansion The layers consisting of different components alternate ( CTE)in the odd layers is smaller than the CtE of one after another, but the external layers consist of the the even ones. The changes in compressive and tensile same component. Thus, the total number of layers N stresses depend on the mismatch of CTE's, Young's in such a composite sample is odd. The layers of the moduli, and on the thickness ratio of layers(even/odd). first component including two external(top) layers are However, if the compressive stresses exist only at or designated by index 1(= 1), and the layers of the near the surface of ceramics and are not placed inside second component(internal)are designated by index the material, they will not effectively hinder internal 2(j= 2). The number of layers designated by index cracks and flaws [ 9] I is (N+ 1)/2, and the number of layers designated Boron carbide is an important ceramic material with by index 2 is(N-1)/2. The layer of each omponent many useful physical and chemical properties. After cu- has some constant thickness, and the layers of same bic boron nitride, it is the hardest boron containing com- component have identical thickness pound [1o]. Its high melting point, high elastic modulus, There are effective residual stresses in the layers of large neutron capture section, low density, and chem- each component in the layered ceramic composite Dur- ical inertness make boron carbide a strong candidate ing cooling, the difference in deformation, due to the for several high technology applications. Due to its low different thermal expansion factors of the components density and superior hardness, boron carbide is a very is accommodated by creep as long as the temperature romising material for light-weight ballistic protection. is high enough. Below a certain temperature, which Boron carbide exists as a stable single phase in a large is called the"joining "temperature, the different com- homogeneity range from B4C to B1o 4C [11]. The most ponents become bonded together and internal stresses that hardness of stoichiometric B4C is the highest one component material are leen l么、sm的。e table boron carbide structure is rhombohedral with a appear In each layer, the total strain after sintering is stoichiometry of B13C2, B12 C3, and some other phases the sum of an elastic component and of a thermal com- close to B12C3 [12, 13]. The Vickers hardness of B4 C is ponent [22, 23]. The residual stress of in the range of 32-35 GPa [ 14]. There is an indication perfectly rigid bonding betw in comparison with boron rich or carbon rich boron car- bide compositions [15-17]. However, B4C-based com E1E2f2(ar2-ar1)△T osites have a relatively low fracture toughness of 2.8- (1) 3.3 MPa-m/2[18]. While high hardness is one of the EIfi+ E?f2 very important requisite indicators for a materials bal listic potential, toughness might play an equally impor- tant role in realizing that potential. Thus, materials with E2E1far1-aT2)△T both high hardness and high fracture toughness are ex- E1f1+E22 pected to yield the best ballistic performance [1, 19 Therefore, a significant increase in fracture toughness where E=Ej/(I-vi), fi=2u, f2=2D2 of boron carbide based laminates has the potential for Ej and v are the elastic modulus and Poisson's ratio of realization of improved armor material systems j-th component respectively, II and l2 are the thickness be controlled by designing the distribution of resid- aT2 are the thermal expansion coefficients(CTE)of ual stresses, i.e., placing the layers with high compres- the first and second components respectively, AT is sive stresses into the bulk of the material. The sign and the difference in temperature of joining temperature value of the bulk residual stresses have to be firmly and current temperature, and w is the total thickness of established by theoretical prediction [20]. A signifi- the specimen cant increase in ballistic protection of B. C based lam Equations l and 2 give the residual stresses in layers inates may be achieved by designing high compressive which have an infinitive extent. Far away from the free stresses placed into the bulk of the materials. The goal of surface, the residual stress in the layer is uniform and this research was to develop the design and processing biaxial. In the bulk of layers, the stress perpendicular to of boron carbide-silicon carbide ceramic laminates with the layers is zero. At the free surface of the laminates, controlled residual stresses. In this article we demon- the stresses are different from the bulk stresses Near strate a laminate design concept by determining the the edges, the residual stress state is not biaxial because prospective combination of layers, their geometry and the edges themselves must be traction-free. Highly lo- microstructure for the B, C/B4 C-30 wt%SiC system, as calized stress components perpendicular to the layer well as a laminates manufacturing route. The appar- plane exist near the free surface and it decreases rapidly ent Klc of three layered composite was measured to be from the surface becoming negligible at a distance ap 7.42+0.82 MPa. m/, but the detailed report on the me- proximately on the order of the layer thickness. These chanical properties, such as Youngs modulus, fracture stresses have a sign opposite to that of the equibiaxial toughness, hardness, and ballistic performance of the stresses deep within the layer. Therefore, if the bulk developed laminates will be presented elsewhere [21]. stress is compressive within the material, the tensile 5484outer layers near the surface increase strength, flaw tol￾erance, fatigue strength, fracture toughness and stress corrosion cracking. In the case of symmetrical lami￾nates, this can be done by choosing the layer compo￾sitions such that the coefficient of thermal expansion (CTE) in the odd layers is smaller than the CTE of the even ones. The changes in compressive and tensile stresses depend on the mismatch of CTE’s, Young’s moduli, and on the thickness ratio of layers (even/odd). However, if the compressive stresses exist only at or near the surface of ceramics and are not placed inside the material, they will not effectively hinder internal cracks and flaws [9]. Boron carbide is an important ceramic material with many useful physical and chemical properties. After cu￾bic boron nitride, it is the hardest boron containing com￾pound [10]. Its high melting point, high elastic modulus, large neutron capture section, low density, and chem￾ical inertness make boron carbide a strong candidate for several high technology applications. Due to its low density and superior hardness, boron carbide is a very promising material for light-weight ballistic protection. Boron carbide exists as a stable single phase in a large homogeneity range from B4C to B10.4C [11]. The most stable boron carbide structure is rhombohedral with a stoichiometry of B13C2, B12C3, and some other phases close to B12C3 [12, 13]. The Vickers hardness of B4C is in the range of 32–35 GPa [14]. There is an indication that hardness of stoichiometric B4C is the highest one in comparison with boron rich or carbon rich boron car￾bide compositions [15–17]. However, B4C-based com￾posites have a relatively low fracture toughness of 2.8– 3.3 MPa·m1/2 [18]. While high hardness is one of the very important requisite indicators for a material’s bal￾listic potential, toughness might play an equally impor￾tant role in realizing that potential. Thus, materials with both high hardness and high fracture toughness are ex￾pected to yield the best ballistic performance [1, 19]. Therefore, a significant increase in fracture toughness of boron carbide based laminates has the potential for realization of improved armor material systems. Brittleness of boron carbide ceramic laminates can be controlled by designing the distribution of resid￾ual stresses, i.e., placing the layers with high compres￾sive stresses into the bulk of the material. The sign and value of the bulk residual stresses have to be firmly established by theoretical prediction [20]. A signifi- cant increase in ballistic protection of B4C based lam￾inates may be achieved by designing high compressive stresses placed into the bulk of the materials. The goal of this research was to develop the design and processing of boron carbide-silicon carbide ceramic laminates with controlled residual stresses. In this article we demon￾strate a laminate design concept by determining the prospective combination of layers, their geometry and microstructure for the B4C/B4C-30 wt%SiC system, as well as a laminates’ manufacturing route. The appar￾ent KIc of three layered composite was measured to be 7.42±0.82 MPa·m1/2, but the detailed report on the me￾chanical properties, such as Young’s modulus, fracture toughness, hardness, and ballistic performance of the developed laminates will be presented elsewhere [21]. 2. Thermal residual stresses and its calculation In this work the two-component brittle layered com￾posites with symmetric macrostructure are considered. The layers consisting of different components alternate one after another, but the external layers consist of the same component. Thus, the total number of layers N in such a composite sample is odd. The layers of the first component including two external (top) layers are designated by index 1 (j = 1), and the layers of the second component (internal) are designated by index 2 (j = 2). The number of layers designated by index 1 is (N + 1)/2, and the number of layers designated by index 2 is (N − 1)/2. The layer of each component has some constant thickness, and the layers of same component have identical thickness. There are effective residual stresses in the layers of each component in the layered ceramic composite. Dur￾ing cooling, the difference in deformation, due to the different thermal expansion factors of the components, is accommodated by creep as long as the temperature is high enough. Below a certain temperature, which is called the “joining” temperature, the different com￾ponents become bonded together and internal stresses appear. In each layer, the total strain after sintering is the sum of an elastic component and of a thermal com￾ponent [22, 23]. The residual stresses in the case of a perfectly rigid bonding between the layers of a two￾component material are [7]: σr1 = E 1E 2 f2(αT 2 − αT 1)T E 1 f1 + E 2 f2 (1) and σr2 = E 2E 1 f1(αT 1 − αT 2)T E 1 f1 + E 2 f2 , (2) where E j = E j /(1 − νj), f1 = (N+1)l1 2w , f2 = (N−1)l2 2w , E j and νj are the elastic modulus and Poisson’s ratio of j-th component respectively, l1 and l2 are the thickness of layers of the first and second component, αT 1 and αT 2 are the thermal expansion coefficients (CTE) of the first and second components respectively, T is the difference in temperature of joining temperature and current temperature, and w is the total thickness of the specimen. Equations 1 and 2 give the residual stresses in layers, which have an infinitive extent. Far away from the free surface, the residual stress in the layer is uniform and biaxial. In the bulk of layers, the stress perpendicular to the layers is zero. At the free surface of the laminates, the stresses are different from the bulk stresses. Near the edges, the residual stress state is not biaxial because the edges themselves must be traction-free. Highly lo￾calized stress components perpendicular to the layer plane exist near the free surface and it decreases rapidly from the surface becoming negligible at a distance ap￾proximately on the order of the layer thickness. These stresses have a sign opposite to that of the equibiaxial stresses deep within the layer. Therefore, if the bulk stress is compressive within the material, the tensile 5484