CRACK GROWTH IN NOTCHED SPECIMEN UNDER REPETITIVE IMPACTS Presented By: Gayan Abeygunawardane-Arachchige Gayan Abeygunawardane-Arachchige Prof. Vadim Silberschmidt Wolfson School of Mechanical & Manufacturing Engineering, Loughborough University, UK 1 Mechanics of Advanced Materials Research Group ISMMS 2015, Augustów, Poland, May 31 – June

Introduction MINING COMPANY LOGINOV AND PARTNERS VIBRO-IMPACT MACHINES BASED ON PARAMETRIC RESONANCE: Concepts, mathematical modelling, experimental verification and implementation VIBRO-IMPACT MACHINES BASED ON PARAMETRIC RESONANCE: Concepts, mathematical modelling, experimental verification and implementation Mechanics of Advanced Materials Research Group

3 Out line 1.Introduction and Motivation  Mining and construction screening process  Concept of parametric resonance (PR)  Effect of notch shapes  Aim of the study 2.Finite Element Method  Calculation of Fracture Energy and impact vel.  Constitutive model  Material Properties  Geometry, BCs of the model  Boundary conditions 3.Results and Discussion  Impact Energy vs Number of Cycles  Von-Mises Stress variation ahead Crack Tip  Shapes of crack paths for different impact Energies  Crack propagation rate for different energy input 4.Conclusions 1.Introduction and Motivation  Mining and construction screening process  Concept of parametric resonance (PR)  Effect of notch shapes  Aim of the study 2.Finite Element Method  Calculation of Fracture Energy and impact vel.  Constitutive model  Material Properties  Geometry, BCs of the model  Boundary conditions 3.Results and Discussion  Impact Energy vs Number of Cycles  Von-Mises Stress variation ahead Crack Tip  Shapes of crack paths for different impact Energies  Crack propagation rate for different energy input 4.Conclusions Mechanics of Advanced Materials Research Group

Introduction  The Purpose of the machine is to filter the mining product by means of parametric vibration.  The screener is a perforated plate which is clamped after pretension  The vibration is achieved by means of motors on the side of the screener  The screen is normally perforated by standard geometrical holes ( circular, rectangular ) 4

Introduction & Motivation 5  Failure of the screener is frequent and requires the substitution of the perforated plate  These failures happen first at the sides of the screener, then at the middle of the plate  The main reason for these failure is associated to the PR conditions, due to the location of the cracks  The effect of the granular particles on the screener are still unknown  Failure of the screener is frequent and requires the substitution of the perforated plate  These failures happen first at the sides of the screener, then at the middle of the plate  The main reason for these failure is associated to the PR conditions, due to the location of the cracks  The effect of the granular particles on the screener are still unknown

Introduction and Motivation(Cont..)  A typical example of Parametric vibration is the swing due to the exchange of angular momentum between the swing and the swinger.  It is suspected that notches created by the holes initiates cracks. 6 Amplitudes of the oscillation of the screener in vertical and horizontal directions

Introduction and Motivation(Cont..)  The critical factor in investigating the failure of the screen is to analyse the effect of notch shapes.  Different geometries contributes different stress concentration levels for peculiar loading conditions 7 Stress Concentration; retrieved from

MODELLING OF CRACK GROWTH FOR REPITITIVE LOADING CONDITIONS /Finite Element Modelling 8

Calculation of Fracture Energy and Impact Velocity  Fracture energy required - 2 γA γ – Surface energy (kJ/m2) A – Fracture surface area  From Schiavone et al. γ=1500 kJ/m 2 and A= rectangular cross section;  This fracture energy should be supplied by means of kinetic energy = 0.5mV 2  m; is taken as 3.14kg (mass of the pendulum)  The velocity to complete fracture with a single impact is 361 mm/s. 9 Schiavone A., G.Abeygunawardane Arachchige, Vadim Silberschmidt, Crack initiation And propagation in ductile specimens with notches, Acta Mechanica, Special Issue Micro mechanics.

Constitutive Modelling 10 f c - Critical value of void volume fraction f F - Critical value of void volume fraction

Material Properties  Material – Al 1050a  Young’s Modulus = 70 Gpa  Poisson’s ratio = 0.33  Hardening characteristic = initial yield stress with 85MPa with multi-linear curve based on experimental tests 11 Source – Schiavone A.2014

Consideration of instrument setup for FE modelling 12

Specimen Geometry, BCs and /FE - Mesh 13 FE-Software - Abaqus/ Explicit 6.14 Element – 4- Node bilinear, 2D plane stress, reduced integration elements.

Fatigue Cycle – Shape and its characteristics 14 Pendulum travels into the specimen along (+y) direction Pendulum reverse the direction from (+) y to (-) y Pendulum travels in negative direction and reach to the initial position Pendulum reverse the direction from (-) y to (+) y Pendulum travels into the specimen along (+y) direction

Calculation of Stress concentration factor 15 For Double edge notched specimen; K I can be calculated as.. Where a and b are length parameters and σ is the applied stress ASME, the analysis of cracks Hand book, Tada et.al.2000

RESULTS AND DISCUSSION /Finite Element Modelling 16

Results and discussion 17 Impact Energy vs Number of Cycles Impact energy reduces in an exponential Way as the number of fatigue cycles increases

Results and discussion 18 Von-Mises Stress Distribution on the course during Crack Propagation ( For N=6 case) N=1N=2 N=3 N=4

Results and discussion 19 Von-Mises Stress Distribution on the course during Crack Propagation ( For N=6 case) N=5 N=6

Results and discussion 20 Shapes of crack path for different impact energies 4% of E1% of E 0.5% of E0.1% of E E – Energy required to break the specimen from single impact

Results and discussion 21 Shapes of crack path for different impact energies 0.06% of E 0.02% of E 0.009% of E

Results and discussion 22 Crack Propagation rate for different energy input

Results and discussion 23 Experimental Results for mixed mode cracks – Al 1050 Employed Push- Pull fatigue tests at a frequency of 10 Hz. Makabe, C., et al. "Evaluation of fatigue crack propagation by mode I and mixed mode in 1050 aluminium.“ Fatigue & Fracture of Engineering Materials & Structures 30.4 (2007):

Results and discussion 24 Crack Propagation rate Vs Stress Intensity factor ( From Simulation )

Conclusion  GTN parameters determined under quasi static conditions was used in this dynamic fatigue analysis.  Based on the previous study (Schiavone et al.) ; two types were observed based on crack propagation direction.  When the input energy is equal and above 1% of E; the crack shape is similar to the crack shape observed for quasi static tensile test. 25

Conclusion  GTN model does not include void distortion and inter void linking in damage evolution.  Though the location of the crack initiation is correct; crack propagation rate is significantly rapid with the GTN model compared with the experiments available. 26