MODELLING OF DEFORMATION AND DAMAGE OF SPECIMENS UNDER STATIC AND DYNAMIC

LOADING

Kondryakov E.A., Lenzion S.V., and Kharchenko V.V.

Tensile tests of smooth cylindrical

specimens

Numerical modelling of Charpy impact tests

Numerical modelling of tensile tests of smooth cylindrical specimens

True stress-strain diagram

Charpy impact tests

GTN model parameters

Comparison of the results

obtained

Schematic of the investigations performed

Specimens used

To determine the GTN model parameters, specimens of steel 45 model material were tested in uniaxial tension. Two types of specimens were used: a smooth

cylindrical specimen and a specimen with a stress concentrator.

Computation scheme for the problem

In the computation finite element scheme the specimen geometry is identical to that of a full-scale specimen used in the experiment. The computation scheme

also includes the loading system gripping unit with the boundary conditions applied. The computation scheme of this kind makes it possible to take into

account the effects of the specimen elasto-plastic deformation in the region of transition from the specimen gauge length to its gripped ends.

Evolution of the smooth cylindrical specimen deformation in the course of modelling

The size and shape of the finite elements in the region of necking influence the calculated stress-strain state. The choice in this domain of finite elements of

rectangular shape elongated in cross direction affords obtaining more accurate results.

Smooth cylindrical specimen

The stress-strain curves obtained by the finite element modelling agree fairly well with the experimental curves. It is

shown that when the computations involve the use

of the GTN-model, the specimen stress-strain curves

come closer to the experimental curves than in the case of a conventional

elasto-plastic model.

Specimen with an R2 stress concentrator

The GTN-model parameters obtained by numerical modelling of a smooth specimen allow a fairly good description of a specimen with a

stress concentrator up to the instant of crack initiation.

Drop-weight impact testing machine

Dynamic testing of Charpy specimens were performed with the use of a drop-weight instrumented impact machine designed and manufactured at the G.S. Pisarenko Institute for Problems of

Strength.

Standard Charpy specimen Design of the drop-weight impact machine supports

Standard Charpy V-notched specimens were used for tests. Steel 45 was used as a model

material.

To obtain more accurate results, the supports were

designed with special recesses on its sides.

Schematic of logging data on specimen loading in impact three-point bend tests Characteristics of ADC NuDAQ PCI 9812/10

Number of input/output channelsNumber of input/output channels - 4 - 4

Maximum sampling frequencyMaximum sampling frequency - 20 М- 20 МHzHz

PrecisionPrecision - 12 - 12 bitbit

Analog input rangeAnalog input range - ±5 В - ±5 В or or ±1 В±1 В

triggertrigger - - analog/digitalanalog/digital

For these tests a multi-channel system was developed for high-speed recording of time variation of forces on the striker and supports and of strains and temperatures, the information for

which is transmitted via an amplification unit and analog-to-digital conversion card to a PC where it is processed with the use of a special program and stored in a tabular and/or graphical form

convenient for further analysis.

The record of load on the impact machine supports in tests of Charpy specimens: a – steel St 45, b – a portion of the signal from Fig. a increased in time,

which corresponds to a crack jump (a region marked by a dashed line).

U, mV

U, mV

t, s

t, s

a

b

Owing to high-speed operation of the system, the region of a drastic drop in the load related to brittle fracture and crack propagation can be

increased on the time scale (200 points per 20 s). This allows us to analyze the peculiarities of load variation during brittle fracture of a specimen and evaluate the crack growth rate. For the given example,

the average rate is ~250 m/s.

Problem computation scheme and a fragment of the finite element partitioning in the notch region

Striker

Specimen

Support

The finite element method-based computations were performed in a dynamical coupled thermomechanical statement for a 2D computation model for the material plane-strain state. Special attention was paid to

the finite-element partitioning of bodies, particularly in the stress concentrator zone. The latter affects very much the computation accuracy. The minimum size of a finite element was 0.016 mm.

Strain rate distribution in the specimen central section at the tip of a notch (or crack of length а) at the loading rate V = 5 m/s at the instant of time: 1 – t = 0.1s, 2 - 0.3 s, 3 - 0.5 s, 4 - 1.0 s (1, 2 – without a crack; 3, 4 – with a crack).

It has been found that in impact tests of Charpy specimens the maximum strain rate at the notch root changes almost linearly with the loading rate in the 1-10 m/s

range and is equal to 1800÷2500 s-1 for a specimen of steel 45 at V = 5 m/s. With the material damage and crack propagation taken into account, the

maximum strain rate decreases appreciably – down to 400÷700 s-1.

2

1

2′

1′

Temperature distribution in the specimen central section at the notch tip for the loading rate V = 5 m/s: а) – in adiabatic heating (1, 2) and with allowance for heat propagation (1′, 2′), b) – at different instants of time

1

2

3

7

4

6

а b

A considerable heating up of the material during deformation is concentrated in a small (of the order of 0.1 mm) region at the notch

(crack) tip. Consideration of the material damage and heat propagation decrease appreciably the maximum value of the

temperature increase.

Computation Experiment

The results obtained from numerical and experimental modelling coincide qualitatively. The slide illustrates crack propagation in the computation model and in a real specimen, as well аs corresponding diagrams. A decrease in the

load after reaching Fmax is associated with a ductile crack growth.

ConclusionsConclusions A method of performing static tests of smooth A method of performing static tests of smooth

specimens and specimens with stress specimens and specimens with stress concentrators in uniaxial tensionconcentrators in uniaxial tension and dynamic and dynamic tests of Charpy specimens with logging of the tests of Charpy specimens with logging of the results results has been developed, tried out, and has been developed, tried out, and refinedrefined..

A method of numerical modelling has been A method of numerical modelling has been developed and refineddeveloped and refined, , computation schemes computation schemes have been constructedhave been constructed..

When analyzing changes in the specimen fracture When analyzing changes in the specimen fracture mode in the course of testing, one should take mode in the course of testing, one should take into account heating up of the material at the tip into account heating up of the material at the tip of the stress concentratorof the stress concentrator..