relative thickness and layers numbers reveals that the ple. The maximum possible apparent fracture tough maxImum crad ielding will be achieved for three- ness of the corresponding layered structure is also de layer composites with an edge crack extending to the termined in all iterations as an indicative parameter of first interface. However, the multilayered design is also the design. The determination of the apparent Klc uses very important to meet specific ballistic requirements. the compressive residual stress and the thickness of a It is essential during impact loading to have more bar- top layer as a crack length at any given iteration. These riers to arrest cracks. In our case it is the number of two parameters( the compressive residual stress and the nly one such barrier that is a top compressive layer. site directions. A decrease in the top layer thickness can compressive layers For a three-layer design there is thickness of the top layer)have trends acting in opp The top layer plays a key role for the projectile defeat, increase the residual stress in the layer, but it decreases however multilayered design is of further importance the length of the maximum crack. Therefore, the max- to stop cracks more effectively. Therefore, we designed imum apparent fracture toughness was always used to and manufactured both three-layered and nine-layered analyze the correct thickness ratio composites in this work. The input parameters of laminate design are the co- 4. Processing of laminates efficients of thermal expansion, Youngs moduli, Pois- The material systems selected for the proposed study sons ratios, and densities of the constituents of lay- were B4C and BC-30 wt% SiCbecause of theirpromise ered composite. A very important but experimentally for ballistic applications [31-33]. Table I shows therel unknown input parameter is also AT-a" tem- evant material properties used in the design calculations perature. The output parameters are layers thickness (compiled from literature), and Tables II and Ill show and composition. The step-by-step design technique to the corresponding calculated residual stresses in the obtain the enhanced fracture toughness of a layered B4C/B, C-30 wt%SiC laminates. The maximum possi- omposite is as follows ble apparent fracture toughness for corresponding lay ered structures is also presented in the Tables Il and Ill 1. The compositions of layers are selected depend- The layers under tensile stress have higher CTE, and in ing on a future application of the composite. Then, the this case they are B4C layers. The layers under com- relevant material constants entering the design are de- pressive stress have lower CTE; here they are B. C- termined 30 wt%SiC layers. A temperature T= 2150C 2. The effective coefficients of thermal expansion, used for the majority of the calculations, when resid an effective Young's modulus, an average density and ual stresses appeared in the layers upon cooling from a thickness ratio of layers are determined using the rule the hot pressing temperature. There is no liquid ph of mixture present during the sintering of B4 C/B4 C-Sic ceram- 3. The next step of design is the selection of the ics [34], therefore, the hot pressing temperature wa er's number It can be any appropriate number de- used as a "joining "temperature AT for calculations nding on the required total thickness of the tile. It should be noted that all laminates were designed in To obtain the enhanced fracture resistance of layered such a way that the tensile stresses had been maintained composite, the factors affecting the apparent fracture at low values toughness should be taken into account. Usually, the B4C and a-SiC powders with a grain size of thickness of the thinnest possible layer is limited by 2-5 um were used for laminates manufacturing. BC the manufacturing technology. Note that a compressive 30 wt% Sic mixtures were made by ball milling the layer should be thin enough to reach high level of resid- respective powders in acetone in a polyethylene bot- ual stress tle using b4c milling media 48 h. The laminates were 4. The ratio of tensile and compressed layer thick- produced via rolling of tapes followed by hot pressing ness(thickness ratio)is determined. Any appropriate The formation of a thin ceramic layer is of specific im- thickness ratio can be used as a first approximation portance, as the sizes of residual stress zones(tensile 5. Tensile layer thickness is found and compressive)are directly connected to the thick- 6. The calculation of residual stresses is fulfilled us- ness of layers. The advantage of rolling, as a method of ing(1)and(2). The total thickness of the sample is also green layers production, are that it allows easy thick determined at this step for a given layer's thickness ratio ness control, achieves high green density of the tapes, aking into account the selected number of layers and requires a rather low amount of solvent and organic 7. The thickness ratio is changed after analysis of the additives as compared to other methods like tape cast- residual stress and the total thickness of the specimen. ing [35]. Additional powder refinement, giving a higher Note that increasing ratio of tensile layer thickness to sintering reactivity, might occur due to large forces ap- oppressive layer thickness decreases tensile residual plied in the pressing zone during rolling. The model stress. However, it can result in increasing total thick- ing of rolling was recently performed that potentially ness of sample. TABLE I Properties of ceramics used in the stress calculation changing thickness ratio, the calculation is re- Such iterations are continued to find a unique Composition E(Gpa) Poissons ratio CTE(10-6K-) layer thickness ratio that produces the maxi ossible compressive residual stress, low tensile sic 483 0.17 5.5 411 0.16 residual stress, and required total thickness of the sam- 5486relative thickness and layers’ numbers reveals that the maximum crack shielding will be achieved for three￾layer composites with an edge crack extending to the first interface. However, the multilayered design is also very important to meet specific ballistic requirements. It is essential during impact loading to have more bar￾riers to arrest cracks. In our case it is the number of compressive layers. For a three-layer design there is only one such barrier that is a top compressive layer. The top layer plays a key role for the projectile defeat, however multilayered design is of further importance to stop cracks more effectively. Therefore, we designed and manufactured both three-layered and nine-layered composites in this work. The input parameters of laminate design are the co￾efficients of thermal expansion, Young’s moduli, Pois￾son’s ratios, and densities of the constituents of lay￾ered composite. A very important but experimentally unknown input parameter is also T – a “joining” tem￾perature. The output parameters are layers thickness and composition. The step-by-step design technique to obtain the enhanced fracture toughness of a layered composite is as follows: 1. The compositions of layers are selected depend￾ing on a future application of the composite. Then, the relevant material constants entering the design are de￾termined. 2. The effective coefficients of thermal expansion, an effective Young’s modulus, an average density and a thickness ratio of layers are determined using the rule of mixture. 3. The next step of design is the selection of the layer’s number. It can be any appropriate number de￾pending on the required total thickness of the tile. To obtain the enhanced fracture resistance of layered composite, the factors affecting the apparent fracture toughness should be taken into account. Usually, the thickness of the thinnest possible layer is limited by the manufacturing technology. Note that a compressive layer should be thin enough to reach high level of resid￾ual stress. 4. The ratio of tensile and compressed layer thick￾ness (thickness ratio) is determined. Any appropriate thickness ratio can be used as a first approximation. 5. Tensile layer thickness is found. 6. The calculation of residual stresses is fulfilled us￾ing (1) and (2). The total thickness of the sample is also determined at this step for a given layer’s thickness ratio taking into account the selected number of layers. 7. The thickness ratio is changed after analysis of the residual stress and the total thickness of the specimen. Note that increasing ratio of tensile layer thickness to compressive layer thickness decreases tensile residual stress. However, it can result in increasing total thick￾ness of sample. After changing thickness ratio, the calculation is re￾peated. Such iterations are continued to find a unique optimal layer thickness ratio that produces the maxi￾mum possible compressive residual stress, low tensile residual stress, and required total thickness of the sam￾ple. The maximum possible apparent fracture tough￾ness of the corresponding layered structure is also de￾termined in all iterations as an indicative parameter of the design. The determination of the apparent KIc uses the compressive residual stress and the thickness of a top layer as a crack length at any given iteration. These two parameters (the compressive residual stress and the thickness of the top layer) have trends acting in oppo￾site directions. A decrease in the top layer thickness can increase the residual stress in the layer, but it decreases the length of the maximum crack. Therefore, the max￾imum apparent fracture toughness was always used to analyze the correct thickness ratio. 4. Processing of laminates The material systems selected for the proposed study were B4Cand B4C-30 wt%SiC because of their promise for ballistic applications [31–33]. Table I shows the rel￾evant material properties used in the design calculations (compiled from literature), and Tables II and III show the corresponding calculated residual stresses in the B4C/B4C-30 wt%SiC laminates. The maximum possi￾ble apparent fracture toughness for corresponding lay￾ered structures is also presented in the Tables II and III. The layers under tensile stress have higher CTE, and in this case they are B4C layers. The layers under com￾pressive stress have lower CTE; here they are B4C- 30 wt%SiC layers. A temperature T = 2150◦C was used for the majority of the calculations, when resid￾ual stresses appeared in the layers upon cooling from the hot pressing temperature. There is no liquid phase present during the sintering of B4C/B4C-SiC ceram￾ics [34], therefore, the hot pressing temperature was used as a “joining” temperature T for calculations. It should be noted that all laminates were designed in such a way that the tensile stresses had been maintained at low values. B4C and α-SiC powders with a grain size of 2–5 µm were used for laminates manufacturing. B4C- 30 wt%SiC mixtures were made by ball milling the respective powders in acetone in a polyethylene bot￾tle using B4C milling media 48 h. The laminates were produced via rolling of tapes followed by hot pressing. The formation of a thin ceramic layer is of specific im￾portance, as the sizes of residual stress zones (tensile and compressive) are directly connected to the thick￾ness of layers. The advantage of rolling, as a method of green layers production, are that it allows easy thick￾ness control, achieves high green density of the tapes, and requires a rather low amount of solvent and organic additives as compared to other methods like tape cast￾ing [35]. Additional powder refinement, giving a higher sintering reactivity, might occur due to large forces ap￾plied in the pressing zone during rolling. The model￾ing of rolling was recently performed that potentially TABLE I Properties of ceramics used in the stress calculation Composition E (Gpa) Poisson’s ratio CTE (10−6 K−1) B4C 483 0.17 5.5 SiC 411 0.16 3 5486