KAJIAN KEPUSTAKAAN
2.7 ANALISIS FAKTOR KEAMATAN TEGASAN RETAK PERMUKAAN
2.7.1 Faktor Keamatan Tegasan Daya Tegangan
ialah fungsi penentukuran plastik penuh dan dipanggil sebagai fungsi-h. Ia penting untuk menganggarkan kamiran-J untuk bentuk dan geometri retak tertentu. Walau bagaimanapun, Lei (2004a; 2004b; 2004c) menyatakan penyelesaian terhadap
fungsi-h masifungsi-h lagi terfungsi-had dan banyak kajian perlu dijalankan untuk tujuan tersebut.
2.7 ANALISIS FAKTOR KEAMATAN TEGASAN RETAK PERMUKAAN
Tinjauan kepustakaan dijalankan ke atas bar berbentuk silinder padu yang mengandungi retak permukaan dengan menggunakan pendekatan mekanik patah anjal-lelurus. Faktor keamatan tegasan (SIF) digunakan sebagai parameter patah yang mana ubah bentuk plastik di sekitar retak berada pada tahap yang paling minimum. Tinjauan kepustakaan ini dijalankan secara berasingan mengikut jenis beban yang dikenakan ke atas bar iaitu daya tegangan, momen lentur dan momen kilas.
2.7.1 Faktor Keamatan Tegasan Daya Tegangan
Rajah 2.8 menunjukkan bar berbentuk silinder yang dikenakan daya tegangan. Retak permukaan adalah terletak di tengah-tengah bar dengan kedalaman dan bentuk retak yang tertentu.
Rajah 2.8 Bar silinder padu yang mengandungi retak dikenakan daya tegangan Dalam menganalisis kelakuan retak berkenaan, SIF ditentukan di sepanjang retak depan retak dan analisis unsur terhingga digunakan untuk tujuan tersebut. Kebiasaanya, SIF dinormalkan untuk mendapatkan SIF yang umum seperti berikut
, , I a I a a K F a (2.19) P P a D
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yang mana, FI,a ialah SIF ternormal daya tegangan, KI,a ialah faktor keamatan tegasan kenaan daya tegangan, a ialah kedalaman retak dan a ialah tegasan tegangan yang diberikan seperti berikut
2 4 a P D (2.20)
yang mana, P ialah daya tegangan yang digunakan dan D ialah garis pusat bar. Pada peringkat awal analisis, retak diandaikan berbentuk lurus (Daoud et al. 1978; Bush 1981; Carpinteri 1992a; Carpinteri 1992b) atau pun berbentuk lengkungan bulat (Daoud & Cartwright 1985; Raju & Newman 1981; Newman & Raju 1979; Raju & Newman 1982; Raju & Newman 1986). Andaian bentuk retak tersebut adalah tidak selari dengan bentuk retak yang diperhatikan daripada ujikaji seperti dalam Rajah 2.9, Rajah 2.10 dan Rajah 2.11. Ini seterusnya menyumbang kepada ketidaktepatan penyelesaian terhadap SIF. Semenjak 30 tahun lalu, masalah yang berkaitan dengan bentuk retak diselesaikan dengan pengenalan kepada lengkungan semi elips untuk memodelkan bentuk retak (Athanassiadis et al. 1981; Astiz 1986; Shiratori et al. 1992; Murakami & Tsuru 1987; Caspers et al. 1990; Carpinteri 1992b; Carpinteri & Brighenti 1996; Couroneau & Royer 1998; Shih & Chen 2002; Shin & Cai 2004).
Carpinteri & Vantadori (2009) kemudiannya mengandaikan bentuk model retak diandaikan seperti Rajah 2.12 untuk dimodelkan seperti dalam pemerhatian eksperimen. Manakala, model retak juga diberikan oleh Shih & Chen (2002) dan Findley et al. (2007) seperti dalam Rajah 2.13. Penyelesaian SIF daripada tinjauan kepustakaan ini menunjukkan untuk retak permukaan dalam rod berbentuk silinder mempunyai beberapa kekurangan. Sebagai contoh, SIF hanya terhad pada titik terdalam retak sahaja dan juga terhad kepada beberapa nisbah bidang retak, a/b dan kedalaman relatif retak, a/D (Daoud & Cartwright 1985; Wilhem et al. 1982; Murakami & Tsuru 1987; Couroneau & Royer 1998; Carpinteri et al. 2000; Iranpour & Taheri 2006; Lin & Smith 1998; Lin & Smith 1999).
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(a) (b)
Rajah 2.9 Mekanisme kegagalan lesu bar, (a) retak semi-elips sebagai permulaan retak dan (b) perambatan retak yang bermula daripada permukaan yang licin
Sumber: Shin & Chai 2004; Findley et al. 2007
(a) (b)
Rajah 2.10 Mekanisme perambatan retak lesu yang bernisbah bidang retak besar dari satu untuk dua jenis tempat permulaan retak, (a) retak bermula di permukaan luar dan (b) retak bermula pada bawah permukaan
Sumber: Findley et al. 2007
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(a) (b)
Rajah 2.11 Permukaan patah (a) bar silinder padu dan (c) plat kenaan momen lentur Sumber: Luke et al. 2011; Liu et al. 2010
Rajah 2.12 Bentuk andaian retak, (a) depan lurus dan (b) semi elips Sumber: Carpinteri & Vantadori 2009
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(a) (b)
Rajah 2.13 Pencirian keratan rentas bar bulat sesatah dengan retak permukaan. (a) retak berbentuk semi-elips dan (b) retak berbentuk depan lurus
Sumber: Shih & Chen 2002; Findley et al. 2007
Tinjauan perkembangan terkini SIF kenaan daya tegangan pada bar berbentuk silinder padu dengan retak permukaan (Toribio et al. 2009a; Toribio et al. 2009b) menunjukkan yang nisbah bidang retak, a/b yang digunakan adalah dalam julat di antara 0.0 hingga 1.0. Dengan perkembangan kemajuan teknologi bahan terkini, bentuk retak dalam julat berkenaan perlu dipertimbangkan semula. Ini adalah kerana berdasarkan kepada pemerhatian ujikaji menunjukkan yang a/b > 1.0 boleh terjadi. Ini adalah salah satu daripada faktor motivasi dalam menjalankan penyelidikan ini seperti dalam Rajah 2.10 dan Rajah 2.14.
Sebagai perbandingan, Rajah 2.15 masing-masing menunjukkan SIF kenaan daya tegangan untuk retak depan lurus dan semi-elips. Untuk retak depan lurus (a/b = 0.0), menunjukkan yang SIF adalah bertepatan di antara satu sama lain sehingga a/D = 0.3. Jika a/D > 0.3, kebanyakan SIF semakin mencapah dan menjauhi di antara satu sama lain. Perbezaan yang lebih ketara berlaku untuk SIF yang didapati daripada Levan & Royer (1993). Manakala, retak berbentuk semi-elips (a/b = 0.5) juga menunjukkan kelakuan yang sama. Ia juga menunjukkan yang Levan & Royer (1993) memberikan keputusan yang lebih tinggi dan Shin & Cai (2004) pula memberikan keputusan yang lebih rendah. Contoh model unsur terhingga yang dikenakan daya tegangan ditunjukan dalam Rajah 2.16.
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