Hart-Smith Elastic-Plastic ModelHart-Smith Elastic-Plastic Model

SE171 Aerospace Structures Repair

Lecture Supplemental Pack 8Lecture Supplemental Pack 8

Instructor: Prof. Hyonny Kim

Department of Structural Engineering

U i it f C lif i S Di

1

University of California, San Diego

Materials contained herein extracted from L.J. Hart-Smith, “Adhesive-Bonded Double-Lap Joints,” NASA CR-112235, 1973

Development of Adhesive Plastic DeformationDevelopment of Adhesive Plastic Deformation

2

Balanced Double-Lap Joint GeometryBalanced Double-Lap Joint Geometry

3

Differential Element of Adherends and AdhesiveDifferential Element of Adherends and Adhesive

Governing Differential Equation –Applicable over entire domain.

4

SolutionSolution Elastic RegionElastic Region

Plastic Region

Constants d and found by bc’s and continuity ofξ0

Constants, d, and τave found by bc s, and continuity of γ at elastic-plastic transition. Also, λ defined as

ξ

For sufficiently long overlaps,

Solution can be simply written as

Plastic Zone Size:

Failure Load:

5

Failure Load:

Critical Shear Strain Energy DensityCritical Shear Strain Energy Density

Strain energy density per unit bond area is:St a e e gy de s ty pe u t bo d a ea s• identified by Hart-Smith as “single necessary and sufficient” parameter for

characterizing the adhesive to define maximum bond strength.Recommends matching area under (typically nonlinear) shear stress vs. strain curve while matching maximum shear stresscurve while matching maximum shear stress.

6

Thermal EffectsThermal EffectsAdherends with CTE mismatch can have thermal stressstress.Adhesive often cured at elevated temperature.Significant “no-load” strains can exist – e.g., cure at 350 °F with operating temp at -67 °F are possible, thus ΔT = -417 °F.Tension vs. compression loading shifts critical location to

7

other side

Thermal Stress SolutionThermal Stress Solution

For moderately long joints, joint strength is lesser value of:

A negative value indicates

and

A negative value indicates failure would occur due to thermal mismatch alone, without application of mechanical load.

where

8

Stiffness Imbalanced AdherendsStiffness Imbalanced Adherends

For moderately long joints:

9

Balancing Adherend Stiffness Results in Strongest JointBalancing Adherend Stiffness Results in Strongest Joint

Stress and Strain Profiles for Unbalanced Joint

10

Peel StressPeel Stress

Exists even for double-lap and thick adherend joints.Peaks at ends of adhesive and contributes to failure initiation within composite layers adjacent to interface.

Peel stress related to outer adherend out-of-plane deflection.

Beam on elastic foundation model used to find wo.

Final result: peak peel stress

11Comment on Hart-Smith’s peel solution: peel stress calculated assuming linear elastic behavior and no interaction with shear stress in plastic zone.

Lower peel stress for thinner to and thicker η

Max value at x = l /2