a key feature that imparts good mechanical properties in the multilayer systems is the ability to be toughened significantly by placing their surfaces in residual compression and to arrest crack. It was shown in [3] that a residual surface compression of -500 MPa in a surface layer of three-layered alumina-zirconia specimen can increase its fracture toughness by a factor of 7.5(up to 30 MPa. m )for edge-crack lengths of the order of the surface-layer thickness. The toughening derived from macroscopic surface compression was, in fact, a crack shielding phenomenon and the fracture toughness increase was equivalent to crack growth resistance (R) behavior [7]. The R-behavior often connected with bridging mechanism. The mechanism is associated with the closure stress field that acts behind the tip of the advancing crack[8. However, there are some differences related to bridging mechanism(this is typical for non-layered ceramics) and the shielding phenomenon in layered structures. Firstly, while bridging mechanism gives rise to dependence of fracture resistance only on crack length increment, the shielding effect results in that fracture resistance depends on overall crack length [3, 7, 9]. Secondly, as a rule the bridging mechanism promotes fracture resistance increasing with crack advance whereas the shielding effect can induce both improvement and deterioration of fracture resistance depending on crack tip location in tensile or compressive layer. Actually layered specimen fracture resistance measured experimentally is the apparent fracture toughnes This is due to superposition of different effects like residual stress shielding and structure inhomogeneity. In fracture mechanics, one usually includes stresses in the crack driving force; however it is sometimes expedient to consider residual stresses as part of the crack resistance. Thus, a higher resistance to failure for layered structure with residual stress is obtained from a reduction of the crack driving force rather than from an increase in the intrinsic material resistance to crack extension [9] Despite numerous experimental and theoretical studies of fracture resistance of MCMC, systematic research of R-behavior and of crack arrest in layered composites are very scarce. a great number of publications deal with symmetrical layered structure. This is an idealized situation. In fact, laminates are characterized by some dissymmetry of their architecture due to random deviations in fabrication process. Moreover, specific non-symmetrical layered structures are important in some engineering applications. Conventional analytical consideration of shielding effect in laminates also neglects difference of elastic moduli of layers [3, 7]. However, effect of different moduli on fracture resistance of laminates is not so negligible. The influence of elastic moduli variation across a layered specimen on R-curve behavior is investigated in [10]. It was shown that the elastic moduli difference affects residual stress distribution and has consequently a significant influence on the measured R-curve behavior. But neither detailed alysis of conditions of crack arresting nor its stable/non-stable growth has been carried out in [10] The effect of macroscopic residual stresses on fracture resistance and crack arresting in non-symmetric Si3N4-based layered structures fabricated in the form of single-edge V-notch-bend(SEVNB)specimens investigated in this study. One of the work goals is application of the compliance technique to study R-curve effect as applied to layered specimens. A special attention is paid to the development of an analytical method to calculate fracture resistance- crack length dependence in layered structures with different elastic moduli of layers. The validit of the method is checked by calculation of the stress intensity factors for edge-cracked layered specimens and comparing the results with the mechanical test data The Model. Figure I shows a scheme of the two-component multilayer specimen analyzed in this study Parameter ti designates thickness of layer number i. The total thickness of specimen of rectangular cross section is w,its width is b, and the total number of layers is N. Choice of coordinate system is important for further consideration. It is the most appropriate to put the coordinate origin on the tensile surface of bending specimen. The geometry of the multilayered material analyzed here is such that the problem can be reduced to one dimension, and that analytically tractable solutions can be used. Here, the parameters of interest in the study of mechanical behavior depend only on coordinate x It was shown in [3, ll] that the stress intensity factor, KI, due to an arbitrary stress distribution in the prospective crack path, in the absence of the crack o(r), can be obtained as a o(r)dx, 292A key feature that imparts good mechanical properties in the multilayer systems is the ability to be toughened significantly by placing their surfaces in residual compression and to arrest crack. It was shown in [3] that a residual surface compression of ~ 500 MPa in a surface layer of three-layered alumina-zirconia specimen can increase its fracture toughness by a factor of 7.5 (up to 30 MPa m⋅ 1 2/ ) for edge-crack lengths of the order of the surface-layer thickness. The toughening derived from macroscopic surface compression was, in fact, a crack shielding phenomenon and the fracture toughness increase was equivalent to crack growth resistance (R) behavior [7]. The R-behavior is often connected with bridging mechanism. The mechanism is associated with the closure stress field that acts behind the tip of the advancing crack [8]. However, there are some differences related to bridging mechanism (this is typical for non-layered ceramics) and the shielding phenomenon in layered structures. Firstly, while bridging mechanism gives rise to dependence of fracture resistance only on crack length increment, the shielding effect results in that fracture resistance depends on overall crack length [3, 7, 9]. Secondly, as a rule the bridging mechanism promotes fracture resistance increasing with crack advance whereas the shielding effect can induce both improvement and deterioration of fracture resistance depending on crack tip location in tensile or compressive layer. Actually layered specimen fracture resistance measured experimentally is the apparent fracture toughness. This is due to superposition of different effects like residual stress shielding and structure inhomogeneity. In fracture mechanics, one usually includes stresses in the crack driving force; however it is sometimes expedient to consider residual stresses as part of the crack resistance. Thus, a higher resistance to failure for layered structure with residual stress is obtained from a reduction of the crack driving force rather than from an increase in the intrinsic material resistance to crack extension [9]. Despite numerous experimental and theoretical studies of fracture resistance of MCMC, systematic research of R-behavior and of crack arrest in layered composites are very scarce. A great number of publications deal with symmetrical layered structure. This is an idealized situation. In fact, laminates are characterized by some dissymmetry of their architecture due to random deviations in fabrication process. Moreover, specific non-symmetrical layered structures are important in some engineering applications. Conventional analytical consideration of shielding effect in laminates also neglects difference of elastic moduli of layers [3, 7]. However, effect of different moduli on fracture resistance of laminates is not so negligible. The influence of elastic moduli variation across a layered specimen on R-curve behavior is investigated in [10]. It was shown that the elastic moduli difference affects residual stress distribution and has consequently a significant influence on the measured R-curve behavior. But neither detailed analysis of conditions of crack arresting nor its stable/non-stable growth has been carried out in [10]. The effect of macroscopic residual stresses on fracture resistance and crack arresting in non-symmetric Si3N4-based layered structures fabricated in the form of single-edge V-notch-bend (SEVNB) specimens is investigated in this study. One of the work goals is application of the compliance technique to study R-curve effect as applied to layered specimens. A special attention is paid to the development of an analytical method to calculate fracture resistance – crack length dependence in layered structures with different elastic moduli of layers. The validity of the method is checked by calculation of the stress intensity factors for edge-cracked layered specimens and comparing the results with the mechanical test data. The Model. Figure 1 shows a scheme of the two-component multilayer specimen analyzed in this study. Parameter ti designates thickness of layer number i. The total thickness of specimen of rectangular cross section is w, its width is b, and the total number of layers is N. Choice of coordinate system is important for further consideration. It is the most appropriate to put the coordinate origin on the tensile surface of bending specimen. The geometry of the multilayered material analyzed here is such that the problem can be reduced to one dimension, and that analytically tractable solutions can be used. Here, the parameters of interest in the study of mechanical behavior depend only on coordinate x. It was shown in [3, 11] that the stress intensity factor, K1, due to an arbitrary stress distribution in the prospective crack path, in the absence of the crack σ( ) x , can be obtained as K h x a x dx a 1 0 = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ∫ , () , α σ (1) 292