How to cite this paper
Berto, F., Torgersen, J & Campagnolo, A. (2017). A review of the fatigue strength of structural materials under multiaxial loading in terms of the local energy density.Engineering Solid Mechanics, 5(4), 245-270.
Refrences
Afshar, R., Berto, F., Lazzarin, P., & Pook, L. P. (2013). Analytical expressions for the notch stress intensity factors of periodic V-notches under tension by using the strain energy density approach. The Journal of Strain Analysis for Engineering Design, 48(5), 291-305.
Aliha, M. R. M., Bahmani, A., & Akhondi, S. (2015). Determination of mode III fracture toughness for different materials using a new designed test configuration. Materials & Design, 86, 863-871.
Aliha, M. R. M., Berto, F., Bahmani, A., Akhondi, S., & Barnoush, A. (2016a). Fracture assessment of polymethyl methacrylate using sharp notched disc bend specimens under mixed mode I+ III loading. Physical Mesomechanics, 19(4), 355-364.
Aliha, M. R. M., Bahmani, A., & Akhondi, S. (2016b). A novel test specimen for investigating the mixed mode I+ III fracture toughness of hot mix asphalt composites–Experimental and theoretical study. International Journal of Solids and Structures, 90, 167-177.
Aliha, M. R. M., Berto, F., Bahmani, A., & Gallo, P. (2017a). Mixed mode I/II fracture investigation of Perspex based on the averaged strain energy density criterion. Physical Mesomechanics, 20(2), 149-156.
Aliha, M. R. M., Berto, F., Mousavi, A., & Razavi, S. M. J. (2017b). On the applicability of ASED criterion for predicting mixed mode I+ II fracture toughness results of a rock material. Theoretical and Applied Fracture Mechanics.
Aliha, M. R. M., & Bahmani, A. (2017). Rock Fracture Toughness Study Under Mixed Mode I/III Loading. Rock Mechanics and Rock Engineering, 50(7), 1739-1751.
Atzori, B., Berto, F., Lazzarin, P., & Quaresimin, M. (2006). Multi-axial fatigue behaviour of a severely notched carbon steel. International Journal of Fatigue, 28(5), 485-493.
Ayatollahi, M. R., Razavi, S. M. J., Moghaddam, M. R., & Berto, F. (2015). Mode I fracture analysis of polymethylmetacrylate using modified energy-based models. Physical Mesomechanics, 18(4), 326-336.
Ayatollahi, M., Berto, F., Campagnolo, A., Gallo, P., & Tang, K. (2017). Review of local strain energy density theory for the fracture assessment of V-notches under mixed mode loading. Engineering Solid Mechanics, 5(2), 113-132.
Bahmani, A., Aliha, M. R. M., & Berto, F. (2017). Investigation of fracture toughness for a polycrystalline graphite under combined tensile-tear deformation. Theoretical and Applied Fracture Mechanics.
Berto, F. (2013). A review on coupled modes in V-notched plates of finite thickness: A generalized approach to the problem. Physical Mesomechanics, 16 (4), 378-390.
Berto, F. (2015a). Crack initiation at V-notch tip under in-plane mixed mode loading: a review of the fictitious notch rounding concept. Physical Mesomechanics, 18(4), 273-282.
Berto, F. (2015b). Some recent results on the fatigue strength of notched specimens made of 40CrMoV13. 9 steel at room and high temperature. Physical Mesomechanics, 18(2), 105-126.
Berto, F., & Barati, E. (2011). Fracture assessment of U-notches under three point bending by means of local energy density. Materials & Design, 32(2), 822-830.
Berto, F., & Lazzarin, P. (2009). A review of the volume-based strain energy density approach applied to V-notches and welded structures. Theoretical and Applied Fracture Mechanics, 52(3), 183-194.
Berto, F., & Lazzarin, P. (2010). On higher order terms in the crack tip stress field. International Journal of Fracture, 161(2), 221-226.
Berto, F., & Lazzarin, P. (2013). Multiparametric full-field representations of the in-plane stress fields ahead of cracked components under mixed mode loading. International Journal of Fatigue, 46, 16-26.
Berto, F., Campagnolo, A., & Ayatollahi, M. R. (2015c). Brittle fracture of rounded V-notches in isostatic graphite under static multiaxial loading. Physical Mesomechanics, 18 (4), pp. 283-297.
Berto, F., Campagnolo, A., & Gallo, P. (2015b). Brittle failure of graphite weakened by V-notches: a review of some recent results under different loading modes. Strength of Materials, 47(3), 488-506.
Berto, F., Campagnolo, A., & Lazzarin, P. (2015a). Fatigue strength of severely notched specimens made of Ti–6Al–4V under multiaxial loading. Fatigue & Fracture of Engineering Materials & Structures, 38(5), 503-517.
Berto, F., Cendon, D. A., Lazzarin, P., & Elices, M. (2013b). Fracture behaviour of notched round bars made of PMMA subjected to torsion at− 60° C. Engineering Fracture Mechanics, 102, 271-287.
Berto, F., Croccolo, D., & Cuppini, R. (2008). Fatigue strength of a fork-pin equivalent coupling in terms of the local strain energy density. Materials & Design, 29(9), 1780-1792.
Berto, F., Kotousov, A., Lazzarin, P., & Pegorin, F. (2013a). On a coupled mode at sharp notches subjected to anti-plane loading. European Journal of Mechanics-A/Solids, 38, 70-78.
Berto, F., Lazzarin, P., & Ayatollahi, M. R. (2013c). Brittle fracture of sharp and blunt V-notches in isostatic graphite under pure compression loading. Carbon, 63, 101-116.
Berto, F., Lazzarin, P., & Kotousov, A. (2011b). On the Presence of the Out–of–Plane Singular Mode Induced by Plane Loading With K II= K I= 0. International Journal of Fracture, 167(1), 119-126.
Berto, F., Lazzarin, P., & Kotousov, A. (2011c). On higher order terms and out-of-plane singular mode. Mechanics of Materials, 43(6), 332-341.
Berto, F., Lazzarin, P., & Marangon, C. (2012b). The effect of the boundary conditions on in-plane and out-of-plane stress field in three dimensional plates weakened by free-clamped V-notches. Physical Mesomechanics, 15 (1-2), pp. 26-36.
Berto, F., Lazzarin, P., & Marangon, C. (2014). Fatigue strength of notched specimens made of 40CrMoV13. 9 under multiaxial loading. Materials & Design, 54, 57-66.
Berto, F., Lazzarin, P., & Wang, C. H. (2004). Three-dimensional linear elastic distributions of stress and strain energy density ahead of V-shaped notches in plates of arbitrary thickness. International Journal of Fracture, 127(3), 265-282.
Berto, F., Lazzarin, P., & Yates, J. (2011). Multiaxial fatigue behaviour of quasi-sharp V-notched specimens made of 39NiCrMo3 steel: a non-conventional application of the local energy. Fatigue and Fracture of Engineering Materials and Structures, 34(11), 921-943.
Berto, F., Lazzarin, P., & Yates, J. (2011a). Multiaxial fatigue behaviour of quasi-sharp V-notched specimens made of 39NiCrMo3 steel: a non-conventional application of the local energy. Fatigue and Fracture of Engineering Materials and Structures, 34(11), 921-943.
Berto, F., Lazzarin, P., Kotousov, A., & Harding, S. (2011d). Out‐of‐plane singular stress fields in V‐notched plates and welded lap joints induced by in‐plane shear load conditions. Fatigue and Fracture of Engineering Materials and Structures, 34(4), 291-304.
Berto, F., Lazzarin, P., Kotousov, A., & Pook, L. P. (2012a). Induced out‐of‐plane mode at the tip of blunt lateral notches and holes under in‐plane shear loading. Fatigue & Fracture of Engineering Materials & Structures, 35(6), 538-555.
Berto, F., Pook, L., & Campagnolo, A. (2017). Corner point singularities under in-plane and out-of-plane loading: a review of recent results. Engineering Solid Mechanics, 5(3), 167-176.
Carpinteri, A., & Spagnoli, A. (2001). Multiaxial high-cycle fatigue criterion for hard metals. International Journal of Fatigue, 23(2), 135-145.
Carpinteri, A., Spagnoli, A., & Vantadori, S. (2009). Multiaxial fatigue life estimation in welded joints using the critical plane approach. International Journal of Fatigue, 31(1), 188-196.
Christopher, C. J., James, M. N., Patterson, E. A., & Tee, K. F. (2007). Towards a new model of crack tip stress fields. International Journal of Fracture, 148(4), 361-371.
Costa, J. D. M., Abreu, L. M. P., Pinho, A. C. M., & Ferreira, J. A. M. (2005). Fatigue behaviour of tubular AlMgSi welded specimens subjected to bending–torsion loading. Fatigue & Fracture of Engineering Materials & Structures, 28(4), 399-407.
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Aliha, M. R. M., Berto, F., Bahmani, A., Akhondi, S., & Barnoush, A. (2016a). Fracture assessment of polymethyl methacrylate using sharp notched disc bend specimens under mixed mode I+ III loading. Physical Mesomechanics, 19(4), 355-364.
Aliha, M. R. M., Bahmani, A., & Akhondi, S. (2016b). A novel test specimen for investigating the mixed mode I+ III fracture toughness of hot mix asphalt composites–Experimental and theoretical study. International Journal of Solids and Structures, 90, 167-177.
Aliha, M. R. M., Berto, F., Bahmani, A., & Gallo, P. (2017a). Mixed mode I/II fracture investigation of Perspex based on the averaged strain energy density criterion. Physical Mesomechanics, 20(2), 149-156.
Aliha, M. R. M., Berto, F., Mousavi, A., & Razavi, S. M. J. (2017b). On the applicability of ASED criterion for predicting mixed mode I+ II fracture toughness results of a rock material. Theoretical and Applied Fracture Mechanics.
Aliha, M. R. M., & Bahmani, A. (2017). Rock Fracture Toughness Study Under Mixed Mode I/III Loading. Rock Mechanics and Rock Engineering, 50(7), 1739-1751.
Atzori, B., Berto, F., Lazzarin, P., & Quaresimin, M. (2006). Multi-axial fatigue behaviour of a severely notched carbon steel. International Journal of Fatigue, 28(5), 485-493.
Ayatollahi, M. R., Razavi, S. M. J., Moghaddam, M. R., & Berto, F. (2015). Mode I fracture analysis of polymethylmetacrylate using modified energy-based models. Physical Mesomechanics, 18(4), 326-336.
Ayatollahi, M., Berto, F., Campagnolo, A., Gallo, P., & Tang, K. (2017). Review of local strain energy density theory for the fracture assessment of V-notches under mixed mode loading. Engineering Solid Mechanics, 5(2), 113-132.
Bahmani, A., Aliha, M. R. M., & Berto, F. (2017). Investigation of fracture toughness for a polycrystalline graphite under combined tensile-tear deformation. Theoretical and Applied Fracture Mechanics.
Berto, F. (2013). A review on coupled modes in V-notched plates of finite thickness: A generalized approach to the problem. Physical Mesomechanics, 16 (4), 378-390.
Berto, F. (2015a). Crack initiation at V-notch tip under in-plane mixed mode loading: a review of the fictitious notch rounding concept. Physical Mesomechanics, 18(4), 273-282.
Berto, F. (2015b). Some recent results on the fatigue strength of notched specimens made of 40CrMoV13. 9 steel at room and high temperature. Physical Mesomechanics, 18(2), 105-126.
Berto, F., & Barati, E. (2011). Fracture assessment of U-notches under three point bending by means of local energy density. Materials & Design, 32(2), 822-830.
Berto, F., & Lazzarin, P. (2009). A review of the volume-based strain energy density approach applied to V-notches and welded structures. Theoretical and Applied Fracture Mechanics, 52(3), 183-194.
Berto, F., & Lazzarin, P. (2010). On higher order terms in the crack tip stress field. International Journal of Fracture, 161(2), 221-226.
Berto, F., & Lazzarin, P. (2013). Multiparametric full-field representations of the in-plane stress fields ahead of cracked components under mixed mode loading. International Journal of Fatigue, 46, 16-26.
Berto, F., Campagnolo, A., & Ayatollahi, M. R. (2015c). Brittle fracture of rounded V-notches in isostatic graphite under static multiaxial loading. Physical Mesomechanics, 18 (4), pp. 283-297.
Berto, F., Campagnolo, A., & Gallo, P. (2015b). Brittle failure of graphite weakened by V-notches: a review of some recent results under different loading modes. Strength of Materials, 47(3), 488-506.
Berto, F., Campagnolo, A., & Lazzarin, P. (2015a). Fatigue strength of severely notched specimens made of Ti–6Al–4V under multiaxial loading. Fatigue & Fracture of Engineering Materials & Structures, 38(5), 503-517.
Berto, F., Cendon, D. A., Lazzarin, P., & Elices, M. (2013b). Fracture behaviour of notched round bars made of PMMA subjected to torsion at− 60° C. Engineering Fracture Mechanics, 102, 271-287.
Berto, F., Croccolo, D., & Cuppini, R. (2008). Fatigue strength of a fork-pin equivalent coupling in terms of the local strain energy density. Materials & Design, 29(9), 1780-1792.
Berto, F., Kotousov, A., Lazzarin, P., & Pegorin, F. (2013a). On a coupled mode at sharp notches subjected to anti-plane loading. European Journal of Mechanics-A/Solids, 38, 70-78.
Berto, F., Lazzarin, P., & Ayatollahi, M. R. (2013c). Brittle fracture of sharp and blunt V-notches in isostatic graphite under pure compression loading. Carbon, 63, 101-116.
Berto, F., Lazzarin, P., & Kotousov, A. (2011b). On the Presence of the Out–of–Plane Singular Mode Induced by Plane Loading With K II= K I= 0. International Journal of Fracture, 167(1), 119-126.
Berto, F., Lazzarin, P., & Kotousov, A. (2011c). On higher order terms and out-of-plane singular mode. Mechanics of Materials, 43(6), 332-341.
Berto, F., Lazzarin, P., & Marangon, C. (2012b). The effect of the boundary conditions on in-plane and out-of-plane stress field in three dimensional plates weakened by free-clamped V-notches. Physical Mesomechanics, 15 (1-2), pp. 26-36.
Berto, F., Lazzarin, P., & Marangon, C. (2014). Fatigue strength of notched specimens made of 40CrMoV13. 9 under multiaxial loading. Materials & Design, 54, 57-66.
Berto, F., Lazzarin, P., & Wang, C. H. (2004). Three-dimensional linear elastic distributions of stress and strain energy density ahead of V-shaped notches in plates of arbitrary thickness. International Journal of Fracture, 127(3), 265-282.
Berto, F., Lazzarin, P., & Yates, J. (2011). Multiaxial fatigue behaviour of quasi-sharp V-notched specimens made of 39NiCrMo3 steel: a non-conventional application of the local energy. Fatigue and Fracture of Engineering Materials and Structures, 34(11), 921-943.
Berto, F., Lazzarin, P., & Yates, J. (2011a). Multiaxial fatigue behaviour of quasi-sharp V-notched specimens made of 39NiCrMo3 steel: a non-conventional application of the local energy. Fatigue and Fracture of Engineering Materials and Structures, 34(11), 921-943.
Berto, F., Lazzarin, P., Kotousov, A., & Harding, S. (2011d). Out‐of‐plane singular stress fields in V‐notched plates and welded lap joints induced by in‐plane shear load conditions. Fatigue and Fracture of Engineering Materials and Structures, 34(4), 291-304.
Berto, F., Lazzarin, P., Kotousov, A., & Pook, L. P. (2012a). Induced out‐of‐plane mode at the tip of blunt lateral notches and holes under in‐plane shear loading. Fatigue & Fracture of Engineering Materials & Structures, 35(6), 538-555.
Berto, F., Pook, L., & Campagnolo, A. (2017). Corner point singularities under in-plane and out-of-plane loading: a review of recent results. Engineering Solid Mechanics, 5(3), 167-176.
Carpinteri, A., & Spagnoli, A. (2001). Multiaxial high-cycle fatigue criterion for hard metals. International Journal of Fatigue, 23(2), 135-145.
Carpinteri, A., Spagnoli, A., & Vantadori, S. (2009). Multiaxial fatigue life estimation in welded joints using the critical plane approach. International Journal of Fatigue, 31(1), 188-196.
Christopher, C. J., James, M. N., Patterson, E. A., & Tee, K. F. (2007). Towards a new model of crack tip stress fields. International Journal of Fracture, 148(4), 361-371.
Costa, J. D. M., Abreu, L. M. P., Pinho, A. C. M., & Ferreira, J. A. M. (2005). Fatigue behaviour of tubular AlMgSi welded specimens subjected to bending–torsion loading. Fatigue & Fracture of Engineering Materials & Structures, 28(4), 399-407.
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