Prediction of Load-Displacement Curve for Weld-Bonded Stainless Steel Using Finite

Element MethodEssam Al-Bahkali

Jonny Herwan

Department of Mechanical EngineeringKing Saud University,

P.O.Box 800, Riyadh 11421, Saudi Arabia

Multiphysics Dec 09-11, 2009

Lille, France

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Background

• It is one of the oldest cost effective, less labor and readily automated electric welding techniques that is used to join similar and dissimilar metals.

• Introducing an adhesive layer in conjunction with a spot weld nugget helps strengthening welded joints and balancing stresses in the weld nugget area.

• Optimum welding quality of a spot welded or a weld-bonded joints, Required optimum welding parameters, i.e. welding current, electrode force, and welding time.

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• The advantages of resistance welding process include – short process times – heat focused at the material interfaces. – easily be automated

• While experimental work provides the necessary physical insight about the behavior of spot-welded joints, predictive tasks such as design; analysis and evaluation of spot-welded structures are often carried out by computational methods

• In predicting stress distribution, stress concentration and failure modes of a weld-bonded or a spot welded nugget, a finite element modeling can do an excellent job in this regard.

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• Engineers use the process of adhesive bonding to join materials

• Adhesive bonding can be used to adhere a wide range of materials such as metal to metal, metal to ceramic, metal to polymer, … etc.

• Some advantages of adhesive bonding– Reducing weight– Uniform stress distribution– Fatigue resistance– Ability to join thick with thin materials as well as the ability to

join dissimilar materials.– No stress concentration

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• There are two types of Bonded structure – Purely Adhesive – Adhesive/Mechanical Connection.

• Bonded-Welded• Bonded-Riveted• Bonded Screwed connections

• The combined connections ensure high fatigue strength of the structures.

• Single lap welded joint is one of the important method used to join two plates together.

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Objective

• In present work – Manufacturing point of view

• To develop a finite element model of weld-bonded that can represent a complete load-displacement curve

• Minimize the experimental or trial in industrial application

– Design point of view

• To obtain the representative weld-bonded model which has reasonable deformation shape and fracture initiation.

• To design the position and the effective number of these joints in the mechanical structures

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The scope of research

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Already done by some researchers:- A. De, et al [2003] - E. Feulvarch, et al [2004]- J. Z. Chen, et al [2006]- There was Sorpass Software that can analyze the

temperature distribution, size of nugget and Heat Affected zone (HAZ)

Process Parameters :• welding current• welding time• electrode force• etc

Size, Properties of Nugget, and

HAZ

Deformation and Fracture of the Joints

Our research !

Experimental Analysis

Finite Element Analysis

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FE Modeling and Boundary Conditions

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F

100 mm30 mm 25 mm

Bonded Model (T.V)

F

100 mm

Bonded Model (F.V)

Adhesive

Strip - B

yx

yx

zx

F

5 mm

Weld-Bonded Model (F.V)

Nugget

Strip - A

Assumptions

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• 3-D FE model • Half of the model was considered to save computation

time• Isotropic adhesive layer• The elastic-plastic FE model was considered in current

analysis for verifying the model with the experimental test

• There is no adhesive layer in a zone 1 mm around the circumference of the welds

• The damage evolutions were chosen arbitrary in term of displacement because the failure propagation is not considered

Finite Element Meshes • The FE mesh was modeled using eight-

node linear brick reduced integration elements for strips and nugget

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Strip - A

Adhesive Part

Transverse direction

Longitudinal direction

Strip - B

Bonded Model

Partial of the Bonded Model

The FE mesh for adhesive layer was modeled using eight-node 3-D cohesive element

• Fine mesh was used in strips around the nugget, nugget, and adhesive layers

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Nugget Part Partial of the Adhesive Model

Partial of the Weld-Bonded Model

Stress Triaxiality

• In Abaqus, the ductile fracture limits are in term of stress triaxiality• The stress triaxiality equation can be written as:

• Where  

• Stress triaxiality can be obtained through equivalent fracture strain. • This can be done by conducting standard tensile test to record the true

strains at the fracture limit.• The value of the stress triaxiality were calculated numerically using

finite element modeling of the notch tensile test

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Hardness Measurement and Indentation Test• Micro-hardness test was used to define the location of the weld nugget and

heat affected zone (HAZ)• The hardness measurement started from the center of the nugget and move

a way from the center to the heat affected zone with a step of 0.25mm.• To obtain the plastic properties of each region, spherical indentation ( 2mm

diameter) was carried out at several loads.• Spherical indentation data can be transferred to true stress-true strain curve

using Ahn-Equation:

• Where

σ is the true stress, ε is the true strain, φ is the plastic constrain factor =3.6, P is the load, Pm is the mean pressure, α is the adjustment constant = 0.14, ac is the contact radius between the indenter and material, R is the indenter radius.

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Micro-hardness and Spherical Indentation Results

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Tensile Test Comparison between Experimental and Finite Element Model

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Load- Displacement Curve of Spot Welding

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Initial Failure Comparison between Experimental and Finite Element Model

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Failure Initiation from Experimental and Finite Element Model at HAZ

Load- Displacement Curve of Adhesive Bonded

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Load- Displacement Curve of Weld-Bonded

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Conclusions• The ductile fracture limit criteria were developed to predict

the deformation and fracture initiation of the model. • Detailed material properties of each zone of resistance spot

welding (nugget, heat affected zone, and base metal) are essential to accurately simulate the model.

• Reverse engineering analysis is introduced to get those material properties by modeling the indentation process using finite element software, and conduct some iteration of models until the load-displacement curve of indentation agree with the experimental curve.

• The results in general for the load-displacements curve from finite element model shows a good agreement with the experimental data.

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