Keywords: notch stress concentration, photo-elasticity, finite elements, vertical slots, horizontal slots.

The photo-elastic method has been employed to determine stress concentrations (SC) in notched plates subjected to in-plane tension combined with compression. Validation and interpretation of the fringe pattern exploits the known solution to the stress raiser in a small circular hole in equi-biaxial tension. These results also compare well with an FE prediction. This has enabled SC's to be determined experimentally for a biaxial stress ratio in plates containing a long, thin slot arranged to be in alignment with each stress axis. The two, principal stresses lying along axes of symmetry in the region surrounding the notch are separated from within each isochromatic fringe by the Kuske method [1]. FE provides a comparable full-field view in which contours of maximum shear stress are identified with the isochromatic fringe pattern. The principal stress distributions show maximum concentrations at the notch boundary with up to a fourfold magnification in the greater of the two applied stresses. Consequently, it is of particular importance to establish the tangential stress distributions around the slot boundary. It is shown that this can easily be achieved from the isochromatic pattern to reveal positions of maximum tension and compression.

It is well known that small holes and slots raise the stress in loaded plates locally by factors of 3 or 4. Clearly this becomes important to an assessment of fatigue life when, in regions of high stress, cyclic loading accelerates the crack initiation process. The various design rules [2] require the SC to be known but often estimate are made for unusual geometries. The problem of crack initiation from holes and slots is an issue of safety in many loaded structures. The prediction of life is possible when the stress raiser is quantified with a stress intensity factor. The finite element technique has been used [3,4] to estimated stress concentration factors in various engineering components where fatigue cracks occur due to the presence of stress concentrations. Holes and slots are less severe than pre-existing cracks but are invariably present in most designs [5,6] appearing with fittings, connections and attachments. Here we shall examine their influence experimentally by the photo- elastic method. Firstly, this method is verified by two alternative methods (i) using the known solution to the stress concentration around a hole in a bi-axially stressed plate and (ii) from a numerical FE simulation. Thereafter, a slot is arranged parallel to the two perpendicular stress axes in turn to establish the severity of its concentration experimentally. Results provide contours of maximum shear stress in the surrounding material. These are separated into major and minor principal stresses along axes of symmetry and around the notch boundary. The degree of concentration is revealed from locating points of maximum tension and compression around the notch boundary.

Holes and slots mm wide and with a maximum length dimension of mm were milled into the centre of mm thick araldite CT 200 photo-elastic sheet. Two methods of bi-axial loading a central, un-gripped mm square area were employed [4] a shear linkage frame and independent application of each perpendicular force with hydraulic jacks. The loading frame test provided a single principal stress ratio and for the latter was adjustable between 0 (uni-axial tension) and . Both plane and circular polariscope arrangements were used with a sodium vapour light. The former was used to identify axes of symmetry within an isoclinic fringe pattern. The latter revealed isochromatic fringes, i.e. lines of maximum shear stress, which were recorded with a mm SLF camera with bellows attachment. A finite element analysis was also conducted using the ABAQUS [9] code.

This study shows that photo-elasticity remains a useful experimental technique for providing a full stress field around notches subjected to bi-axial loadings. The technique may be used to validate FE predictions having it self been validated from known classical elasticity solutions. When slots are aligned with applied stress axes their straight boundaries distribute tangential stress uniformly in tension and compression. A maximum concentration in stress usually occurs within the end radius, their precise position depending upon the slot orientation.

1

Kuske, "A. Photoelastic Stress Analysis", Wiley, 1974.

2

Neuber, H. "Theory of Notch Stresses", J.W.Edwards, 1946.

3

Bahai, H. "A Parametric Model for Axial and Bending Stress Concentration Factor API Drillstring Threaded Connectors", International Journal of Pressure Vessels and Piping, vol. 78 (7), 2001, pp. 495-505. doi:10.1016/S0308-0161(01)00060-6

4

Tranxuan, D., "Optimum fillet radius for a latch", Computer & Structures, v61, Nov. 1996, p645 � 650. doi:10.1016/0045-7949(96)00042-9

5

ESDU, 85045, "Stress Concentrations: Interaction and stress decay for selected cases", December 1985.

6

Linda, K., Uemura, T., "Stress Concentration factor formula widely used in Japan", Fatigue & Fracture of Engineering materials & Structures, v19, n6, June 1996.

7

Taylor, S., "Photoelastic Examination of Stress Concentration", B.Eng Project Report, Brunel University, 1999.

8

Hendry, A.W. "Photoelastic Analysis", Pergamon 1966.

9

Timoshenko, S. and Goodier, J.N., "Theory of Elasticity", McGraw-Hill, 1970.

10

ABAQUS Standard 5.8 user manual, 1998, HKS Inc.

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