Stress Analysis of Crane Hook and Validation by Photo-Elasticity

Crane Hooks are highly liable components and are always subjected to failure due to accumulation of large amount of stresses which can eventually lead to its failure. To study the stress pattern of crane hook in its loaded condition, a solid model of crane hook is prepared with the help of CMM and CAD software. Real time pattern of stress concentration in 3D model of crane hook is obtained. The stress distribution pattern is verified for its correctness on an acrylic model of crane hook using Diffused light Polariscope set up. By predicting the stress concentration area, the shape of the crane is modified to increase its working life and reduce the failure rates.


Introduction
Crane Hooks are highly liable components that are typically used for industrial purposes.It is basically a hoisting fixture designed to engage a ring or link of a lifting chain or the pin of a shackle or cable socket and must follow the health and safety guidelines [1][2][3][4].Thus, such an important component in an industry must be manufactured and designed in a way so as to deliver maximum performance without failure.Thus, the aim of the project is to study the stress distribution pattern of a crane hook using finite element method and verify the results using Photo elasticity.

Failure of Crane Hook
To minimize the failure of crane hook [5], the stress induced in it must be studied.Crane is subjected to continuous loading and unloading.This causes fatigue of the crane hook but the fatigue cycle is very low [6].If a crack is developed in the crane hook, it can cause fracture of the hook and lead to serious accident.In ductile fracture, the crack propagates continuously and is more easily detectible and hence preferred over brittle fracture.In brittle fracture, there is sudden propagation of the crack and hook fails suddenly [7].This type of fracture is very dangerous as it is difficult to detect.
Strain aging embrittlement [8] due to continuous loading and unloading changes the microstructure.
Bending stress and tensile stress, weakening of hook due to wear, plastic deformation due to overloading, and excessive thermal stresses are some of the other reasons for failure.Hence continuous use of crane hooks may increase the magnitude of these stresses and ultimately result in failure of the hook.

Methodology of Stress Analysis
The analysis is carried out in two phase: 1) Finite element stress analysis of an approximate (acrylic) model and its verification by photo elasticity theory 2) Analytical analysis assuming hook as a curved beam and its verification using Finite element analysis of the exact hook.To establish the finite element procedure a virtual model similar to the acrylic mode is prepared in ANSYS and the results of stress analysis are cross checked with that of photo elasticity.After establishing the procedure a virtual model similar to actual crane hook sample is created using CAD software and the results of finite element analysis are now verified with that of analytical method.

Theory of Photo Elasticity
For the verification of the results obtained from FEM, the experimentation is conducted using the concept of photo elasticity.The concept is used to determine stress distribution and stress concentration factors in irregular geometries.The method is based on the property of birefringence, which is exhibited by certain transparent materials.Birefringence is a property by virtue of which a ray of light passing through a birefringent material experiences two refractive indices.Thus, a crane hook model made out of such material is selected for the.

Stress Optic Law
When plane polarized light passes through a photo elas-he model has geometry similar to tha structure on which stress analysis is to be performed.This ensures that the state of stress in the model is similar to that of the structure.tic material, it resolves along the two principal stress directions and each of these components experiences different refractive indices [11].The difference in the refractive indices leads to a relative phase retardation between the two component waves.The magnitude of the relative retardation is given by the stress optic law: where R is the induced retardation, C is the stress optic pola ation of disc is done to find the material fringe va w value, coefficient, t is the specimen thickness, σ 11 is the first principal stress, and σ 22 is the second principal stress.The two waves are then brought together in a riscope set up.Thus, the state of stress at various points in the material can be determined by studying the fringe pattern.
Calibr lue f σ .An acrylic model of disc is taken and subjected to compressive load in the circular polariscope setup.gnitude at a point is given by: (σ 1 -σ 2 )/2 = N f σ / re σ 1 = major principal stress, σ 2 = minor principal

Results
For the approximate model of crane hook, stresses in-  value obtained from ANSYS = 12.3 obtained experimentally = 11.121N/mm 2 .The results are closely in agreement with a very small percentage error = 5.76%.
Possibl at it is difficult to find the magnitude of stress exactly on the plane of the fringe closest to inner surface and thus the value 12.35 may not be accurate.Figure 5 shows the exact location of maximum stress on the approximate model of crane hook as obtained from AN-SYS software.
The above re ell established and can be used for complex and accurate models also.Hence in the second phase of the study, analytical calculations are carried out for the exact model of crane hook and the results are validated from that of ANSYS.

Analytical Method
ory of bending for shallow, straight beam does not yield accurate results.Stress distribution across the depth of such beam, subjected to pure bending, is non linear (to be precise, hyperbolic) and the position of the neutral surface is displaced from the centroidal surface towards the centre of curvature.In case of hooks as shown in Figure 6, the members are not slender but rather have a sharp curve and their cross-sectional dimensions are large compared to their radius of curvature.
The strain is clearly zero at the neutral axis and is maximum at the outer radius of the beam.Using the relationship of stress/strain = E, the normal stress is simply.
The location of the neutral axis is obtained by equating the product of the normal stress and the area elements over the whole area to 0 The stress resulting from an applied bending moment is d the fact, that the resisting moment is sim erived from ply the integral of the product of moment arm over whole section from the neutral axis and σdA.The maximum stress occurs at either the inner or outer surface.
The centroid of the section is . where The maximum stress occurs at either the inner or ou surface: Stress at inner surface ter ., . .

 
The curved beam flexure form la is in reasonable agreement for beams with a ratio of curvature to beam dept r h 8(a ured for the modeling in ANSYS software.u h ( c / ) > 5 (rectangular section).As this ratio increases, the difference between the maximum stress calculated by curved beam formula and the normal beam formula reduces.The above equations are valid for pure bending.In case of crane hooks, the bending moment is due to forces acting on one side of the section under consideration.For calculations the area of cross section is assumed to be trapezoidal [13].Values of stresses as shown in Figure 7 are found out at the A-A section as it is the section where maximum stress is induced.Pro-E software.The virtual model prepared in Pro-E software is i llowing e steps of FEM as discussed earlier the stress analysis obtained from analytical calculaed in the Section 7, are compared with results obtained by FEA software.

Results
The induced stresses as tions, explain ANSYS v/s analytical Max value obtained analytically=12.35N/mm 2 while value obtained from ANSYS = 13 2 The results are in clo ntage error = (13.372-12.35)/12.35= 8.26% Possible reasons for variation might be the d sumption that 1) Loading is considered as point loading in analytical calculation while it is taken on a bun nodes in ANSYS.2) Cross sectional area is assumed to be trapezoidal and 3) Plane sections remain plane after deformation.
Using analytical calculations the stress variation yields the results as shown in   Reasons for variation: Various assumptions made during the analytical calculations (discussed earlier).
Profile of the hook obtained from Pro-E Modeling software may not be exactly the same as actual one.

Conclusions
The complete study is an initiative to establish a FEA procedure, by validating the results, for the measurement of stresses.For reducing the failures of hooks the estimaimportant.Analytical calculation becomes comre too complicated.
rging is preferred to casting as been in casting the molten metal when solidifies, it has some tion of stresses, their magnitudes and possible locations are very plex as the newer designs a Suggestions to reduce failure Manufacturing process: Fo the crane hooks produced from forging are much stronger than that produced by casting.The reason residual stresses due to non uniform solidification.Thus casted crane hooks cannot bear high tensile loads.
Grain size: The stress bearing capacity depends on the homogeneity of the material i.e. the relative sizes of the grains in various areas of the component.Smaller the grain size better is the stress bearing capacity.So grain refinement process such as normalizing is advisable after forging.
Processes such as welding should be avoided as they increase the stress concentration points which eventually lead to failure.
Removal of metal from the hook body is not feasible as it increases the amount of stresses in the hook.This is validated by the following illustration: It is clear from the Design improvement: From the stress analysis we have observed the cross section of max stress area.If the area on the inner side of the hook at the portion of max stress is widened then the stresses will get reduced.Analytically if the thickness is increased by 3 mm, stresses are reduced by 17%.Thus the design can be modified by increasing the thickness on the inner curvature so that the chances of failure are reduced considerably.

Figure 2 .
Figure 2. Principle stresses in the model.

Figure 3
Figure 3. stress pattern of photo elastic model under sodium light.

4 ,
maximum principal stress Stress ma t whe stress, t = thickness of hook.duced during finite element analysis are compared with that of photo elasticity experiment.For the acrylic model of crane hook the results are as under: ANSYS v/s Experimental As shown in Figure

Figure 4 .
Figure 4. Stress distribution pattern for acrylic model (a)

.
372 N/mm se harmony with a small perce ue to the as ch of ensile stress is 150.72 N/mm on the inner su /mm .As shown in Fi 6)/135.46= 10.12%N/mm ; Stress analyti-= 1.01 % mported in ANSYS environment.Fo th is conducted for the actual model in ANSYS environment and the results are obtained.

Figure 8 (
b) shows the magnitude and location of stress.

Figure 9 .
Figure 9. Variation of Stress with depth for the actual model.

Fig 10 (
a) that removal of a small amount of material from minimum stress concen-Ca-[6] Fatigue Cycle.ic.iastate.edu/~gkstarns/ME417S. Suresh, "Fatigue Crack dy of the Structural Relaxa-Tion-Induced Embrittlement of Hypoeutectic Zr-Cu-Al Gro ure tration areas increases the stress slightly though reducing the cost of material.The Figure10(b) validates the fact that when considerable amount of material is removed stresses increase by a good enough margin which is not at all feasible.