For plane stress condition:
?_F =?( (E G_C)/?a)?^(1/2) ;
a: halt of crack length ; GC : fracture energy;
the mere useful parameter in the plane stress condition is critical stress intensity factor (KC) which is defined in a wide sheet ( infinite width ): K_C= ?_F ?(?a)?^(1/2) or
K_C= ?(E G_C)?^(1/2)
To determine KC, it is required to measure (?F) value at which a crack of length (2a) in a thin wide plate begins to propagate. The use of KC to determine whether or not a given thin sheet will fracture under a stress (?) implied provided that the size of the largest crack in the sheet is known to the designer.
The stress intensity factor ( K= ? (?a)^(1/2)) can be computed and compared with (KC); the crack will not spread for ( K < KC ).
Plane strain occurs in thick plate
For a thick plate of infinite width containing a crack of length (2a), the fracture stress is:
?_F= ?((E G_IC)/(? (1-v^2 )^a ))?^(1/2) (plane strain condition)
v=poisson^ sratio,
K_C= ?_F ?(?a)?^(1/2) or K_C= ?((E G_C)/( (1-v^2)))?^(1/2)
In the design calculation of fracture stress, plane strain is normally the best assumption, because materials show minimum toughness, so G_IC < G_C ; K_IC < K_C.
If a component will not fracture in plane strain, it will certainly not fracture in plane stress. The stress intensity factor in plane strain under stress (?) for a wide plate containing a crack of length (2a) is :
K_I= ? ?(?a)?^(1/2)
For KI < KIC the plate will not fracture. The parameters which describe plane strain fracture are GIC and KIC , the subscript (I) refers to the method of opening the crack assumed here where there is two modes of fracture have been defined both involving shear on the crack plane. In mode II, shear is parallel to the crack propagation direction. In mode III, shear is normal to the propagation direction. These types of fracture are important in long fiber composites and in adhesives because of anisotropy. They are of minor importance in thermoplastics.
Cracks in isotropic materials tend to turn in a direction normal to the tensile stress giving mode ( I ) fracture, whether the initial orientation of the crack plane.
Question (H. w) A plate of polystyrene of width (100 mm) contains a central sharp crack of length (40 mm), the crack is found to propagate at 3.9/Mpa. Find (1) critical stress intensity factor. (2) will a central crack of kength (14mm) in an identical plate propagate under 9 Mpa? (3) will a crack of length (3mm) in an infinitely wide polystyrene plate propagate under a stress of 10 Mpa?.
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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