Matlamat utama kajian ini adalah untuk memahami ciri-ciri kehilangan kekangan tiga dimensi dan melanjutkan pencirian skema anggaran kehilangan kekangan tiga dimensi seperti kaedah π½βππ§ dan π½βΞπ dalam retakan. Skema anggaran kehilangan kekangan tiga dimensi dalam medan di hujung retakan elastik plastik telah disiasat dalam kajian ini dengan menggunakan bar retak bawah beban lenturan (SENB) dan plat retak tengah bawah beban tegangan (CCP). Model tersebut telah ditakrifkan dengan sifat bahan pengerasan terikan, π=3,6,13 dan sifat bahan tanpa pengerasan (πββ). Kehilangan kekangan dalam medan tegasan di hujung retakan didapati berubah dalam model dengan panjang retakan yang berlainan, π/π=0.1,0.2,0.3,0.5 and ketebalan yang berbeza, π΅/(πβπ)=0.05,1.
Kehilangan kekangan di hujung retakan telah dikaji melalui pembandingan antara medan tegasan asimptotik bersifat tanpa pengerasan dengan penyelesaian hujung retakan terikan satah medan Prandtl dan penyelesaian hujung retakan tegasan satah Sham & Hancock. Kehilangan kekangan dalam satah didapati bertambah dengan tegasan π negatif apabila nisbah π/π dikecilkan. Penurunan ketebalan model juga didapati mengurangkan kehilanagan kekangan dalam satah kerana tegasan π meningkat dalam model yang nipis. Kehilangan kekangan luar satah diperhatikan di kawasan dari satah tengah ke permukaan bebas dalam semua model. Medan tegasan di permukaan bebas tidak dapat mencapai keadaan tegasan satah penuh kerana dipengaruhi oleh medan singulariti penjuru. Medan tegasan deviatorik adalah unik dalam semua model dan tidak bergantung pada kehilangan kekangan dalam satah dan luar satah. Skema anggaran kehilangan kekangan juga dikemukakan untuk tegasan lingkar di depan retakan dengan menghubungkaitkan kehilanagan kekangan dengan magnitud tegasan π.
Keberkesanaan kaedah π½βππ§ dan kaedah π½βΞπ dalam mencirikan medan di hujung retakan tiga dimensi juga dibincangkan. Pemerolehan terperinci dan algorithma untuk mengira kaedah π½βππ§ telah ditunjukkan. Kaedah π½βππ§ didapati bahawa gagal menggambarkan medan di hunjung retakan model yang menunjukkan kehilangan kekangan dalam satah. Kaedah π½βππ§βπ juga dikesahkan dengan mengunakan parameter π terikan satah. Kaedah π½βππ§βπ didapati bahawa membuat anggaran berlebihan tentang kehilangan kekangan dalam satah dalam model nipis yang menunjukkan tegasan π negatif seperti model CCP nipis. Manakala, kaedah π½βΞπ adalah lebih bermanfaat kerana dapat menyifatkan kehilanagan kekangan dalam dan luar satah secara bersepadu dengan memplotkan tegasan paksi terhadap π½πππ/π§π0 parameter. Penggunaan kaedah π½βππ§ memerlukan pertaburan ππ§ di depan retakan. Sebaliknya, aplikasi kaedah π½βΞπ adalah lebih mudah kerana kehilangan kekangan sepanjang retakan dapat dianggarkan melalui satu lengkungan unik untuk model yang mempunyai ketebalan yang berbeza.
The primary goal of this study is to determine the three-dimensional constraint loss behavior and further extend the three-dimensional constraint loss estimation schemes of π½βππ§ and π½βΞπ approaches in three-dimensional crack tip fields consisting of various crack configurations. The three-dimensional constraint loss estimation schemes in elastic-plastic crack tip fields were examined for a single edge notched bend bar (SENB) and a center cracked panel in tension (CCP). The finite element models were characterized with a strain hardening material, π=3,6,13 and a non-hardening material, πββ. The crack tip constraint loss was found to vary in the models with various crack length, π/π=0.1,0.2,0.3,0.5 and different thicknesses, π΅/(πβπ)=0.05,1.
Crack tip constraint loss was studied by comparing the non-hardening crack tip asymptotic fields with the plane strain Prandtlβs crack tip fields solutions and the plane stress Sham & Hancockβs crack tip solutions. The in-plane constraint loss increased with a more negative π-stress following the reduction of π/π ratio. The thin model exhibited smaller the in-plane constraint loss as π-stress was less negative. The out-of-plane constraint loss occurred in all models at the region away from the midplane to the free surface. The radial and angular distribution of deviatoric stress field ahead of the crack tip was also found to be unique in all models and independent of the in-plane and the out-of-plane constraint loss. A constraint estimation loss scheme at π=0β was proposed for the hoop stress along a crack front by correlating the constraint loss to the magnitude of the π-stress.
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A detailed derivation and an algorithm to compute the π½βππ§ approach were shown. The π½βππ§ approach was unable to characterize the crack tip fields in the models that feature in-plane constraint loss and at the free surface due to a corner singularity field. The π½βππ§βπ approach using a plane strain π parameter was evaluated. It was found that the π½βππ§βπ approach overestimated the in-plane constraint loss in a thin model with negative π-stress as seen in the thin CCP model. New equations were developed to extend the π½βΞπ approach in strain hardening models. The extended π½βΞπ approach offered a unified characterization of the in-plane and out-plane constraint loss along a crack front by plotting the normal stresses against a dimensionless π½πππ/π§π0 parameter. Unlike the π½βππ§ approach that required an exact distribution of ππ§ along a crack front, the π½βΞπ approach is more advantageous as it can be applied immediately to approximate the constraint loss along a crack front by using a unified curve for the models with different thicknesses.
Constraint loss estimation schemes in deep and shallow three-dimensional crack tip fields _Leong Karh Heng_E3_2017_MFAR