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The application of fracture mechanics to polymers and composites allows the quantitative description of the toughness behaviour by means of fracture mechan­ ics parameters and enables preventive failure analysis. In recent years this young scientific discipline has developed rapidly, and now the experimental results are looking for more applications in industrial practice. However, the practical appli­ cations of fracture mechanics parameters to structural-integrity assessment are severely restricted owing to their limited transferability from specimens to com­ ponents. Indeed, geometry-independent fracture mechanics parameters are very important for the reliable functioning of polymers and components in nearly all industrial application fields. These application fields include the polymer development, quality control, con­ struction and polymer-specific design of reliable components in the motor indus­ try, the electrical industry and the manufacture of household appliances, as well as applications in information technology and medical applications. The present status report on the deformation and fracture behaviour of polymer materials was composed on the basis of revised lectures presented at the Merse­ burg discussion conference entitled 'Deformation and Fracture Behaviour of Polymers' and additional single contributions. The editors and authors have tried hard to present information about the applied fracture mechanics of polymers and composites in the light of their current re­ search work.



Characterization of Toughness Using Fracture Mechanics Methods


State of the Art and Development Trends

A 1.1. New Developments in Toughness Evaluation of Polymers and Compounds by Fracture Mechanics

The application of fracture mechanics to the estimation of the failure reliability of products made of polymers and compounds, as well as an evaluation method for quality control and material development, requires geometry-independent parameters which react extraordinarily sensitively to structural changes in the materials. An essential prerequisite for a theoretically well-based material optimization is a knowledge about the connections of strength- and toughness-determined deformation and fracture mechanisms to structural quantities.

W. Grellmann

A 1.2. Concepts of Fracture Mechanics for Polymers

The concepts of fracture mechanics received increasing interest during the last 60 years, when large objects such as ships, tanks and jets suddenly fractured in service, although on the basis of the conventional data for stiffness and strength this failure should not have happened [1]. Microdefects and flaws in the materials have been identified as the origin of this unexpected failure. These defects, which in nearly every material grow to an over-critical size during use of the item, fmally become unstable and initiate a catastrophic fracture. Consequently, it has become urgent to study the instability of cracks, which is the subject of fracture mechanics.

F. Ramsteiner, W. Schuster, S. Forster

Experimental Methods

A 2.1. Influence of Specimen Geometry and Loading Conditions on the Crack Resistance Behaviour of Poly(vinyl chloride) and Polypropylene

The concepts of elastic—plastic fracture mechanics have proved their worth in to characterizing the toughness of thermoplastic polymers. Two different parameters can be used for the characterization of the elastic—plastic material behaviour. These are the energy-determined J-integral and the deformation-determined critical crack-opening displacement.

W. Grellmann, S. Seidler, K. Jung, M. Che, I. Kotter

A 2.2. Procedure for Determining the Crack Resistance Behaviour Using the Instrumented Charpy Impact Test

The instrumented Charpy impact test is used for determining properties related to the impact strength of plastics. It is an addition to the conventional pendulum impact test described in ISO 179 [1]; it is carried out on razor-blade-notched specimens. The plastics on which it can be used range from brittle thermosets to high-impact polymer blends. Both the load and the deflection signals are recorded, and the impact energy is divided into an elastic and a plastic part. If the requirements on the specimen size and on the notch are satisfied, geometry-independent material parameters can be calculated. These parameters can be used for control and for quality assurance as well as for research and development.

W. Grellmann, S. Seidler, W. Hesse

A 2.3. Possibilities and Limits of Standards and Drafts for J—R Curve Determination of Polymers

The fracture mechanics behaviour of polymer materials has been intensively researched in recent years [1–4]. However, the test results have not been fully understood yet. Furthermore, the practical applications of fracture mechanics parameters to assessment of structural integrity are very restricted owing to their limited transferability from specimens to components. Moreover, with the exception of the ESIS TC4 recommendation for plastics [4,5], no standardized test procedures for carrying out fracture toughness testing on tough polymer materials exist, and hence methods developed for metallic materials have simply been adopted. All of this has induced great efforts to seek geometry-independent fracture mechanics parameters.

S. Seidler, W. Grellmann

A 2.4. The Relationship Between the Fracture Behaviour and Structural Parameters of PE-HD

Structural and morphological parameters, together with processing conditions, determine the type of fracture behaviour that occurs in polyethylene. Long-time brittle failure, which occurs under low stresses and at room temperature, limits the lifetime of polyethylene pipes used for water and gas distribution. In order to optimize the lifetime of such pipes, it is necessary to apply methods aimed at a comprehensive understanding of their structure and their fracture properties [1,2].

E. Nezbedová, J. Kučera, Z. Salajka

Alternative Methods

A 3.1. Application of Single-Specimen Testing Methods for Determining J—R Curves of Polymers

Fracture mechanics materials testing allows the determination of characteristic values which can be adapted to the behaviour of structures under real loading conditions, and it can ensure adequate safety with respect to the different possible modes of failure. Depending on the material behaviour, different fracture mechanics parameters can be used; the concept of crack resistance has been shown to provide a quantitative description of the fracture behaviour of ductile thermosets [1]. The critical crack initiation values determined on the basis of the various standards and drafts [2–6] are of special practical value.

S. Seidler

A 3.2. Application of Normalization Method for Determining J—R Curves in the Amorphous Polymer PVC

The increased industrial application of thermoplastics as engineering plastics has resulted in an increase of fracture mechanics research on polymer materials [1–5]. The fracture of polymers may become a decisive factor in material selection and their crack resistance, especially against stable crack growth, determines their usefulness in many applications (pp. 3–26, [6]). Therefore, much work has been done to develop effective evaluation methods for polymers and composites. For tough polymers that exhibit strong viscoelastic behaviour or significant plastic crack tip deformation during the process of fracture, elastic—plastic fracture mechanics (EPFM) methods have been successfully used to describe the fracture behaviour under quasi-static loading [7,8] and under dynamic loading [9,10].

M. Che, W. Grellmann, S. Seidler

A 3.3. Calculation of J—R Curves Based on Load—Deflection Diagrams Using the Hinge Model Test Specimen

One of the main fields of application of fracture mechanics is materials development. In order to avoid problems in the behaviour of components arising from the materials, theoretically founded material optimization can be performed with the help of fracture mechanics concepts combined with morphological investigations. The various characteristic toughness parameters have proved, in materials science practice, to be sensitive indicators for the selection or development of materials.

R. Steiner, W. Grellmann

A 3.4. An Alternative Method Based on J—T J and δ—T δ Stability Assessment Diagrams to Determine Instability Values from Crack Resistance Curves

Recently, the improvement of stiffness and strength and the optimization of toughness behaviour have become an important focus of engineering science because of the expanding fields of application of polymeric materials not only for common, but also for constructional purposes [1]. Measurement of crack resistance curves (R-curves) using the stop block method with the multiple-specimen technique and analysis of R-curve data by means of various procedures are well established for the evaluation of toughness levels, especially those expressed as resistance against initiation and propagation of stable cracks [2–4]. However, the relatively large amount of time required for measuring and analysis and the expensive personnel involved work against considerations of economy. Hence, many research groups have been working intensively on developing approximate R-curve determination methods and on their application to polymeric materials [2,5–7]. Because of limits on the specimen geometry in standard fracture mechanics specimens and because of the loading conditions used, unstable crack propagation can often not be observed. In such cases it is also of interest to calculate material parameters describing the crack instability point [8].

R. Lach, W. Grellmann

Morphology—Property Correlations



B 1.1. Supermolecular Structure and Mechanical Behaviour of Isotactic Polypropylene

The kinetic theory of rubber elasticity has successfully explained the macroscopic mechanical behaviour of polymer networks starting from the thermodynamics of individual molecules [1]. This approach, however, cannot be applied to semicrystalline polymers, where several levels of structural hierarchy can be distinguished, starting from molecular architecture and going up to supermolecular morphology and the macroscopic geometry of a body. Four basic levels of structural hierarchy in isotactic polypropylene are schematically shown in Fig. Bl [2]. In the case of rubber-modified polypropylene, the embedded rubber particles form an additional structural level. The individual structural levels reflect not only the composition but also the thermal and deformation history of the material.

M. Raab, J. Kotek, J. Baldrian, W. Grellmann

B 1.2. Correlation Between Structure and Toughness Behaviour of High-Density Polyethylene under Impact Load

The crack initiation and crack propagation mechanisms of semicrystalline polymers have not been completely resolved. The blunting process in polymers is influenced by many factors determined by the structure [1,2]. The various ideas about the actual blunting process in polymers are described in [3]. A decisive improvement is expected if structural aspects can be included in the examination of micro-mechanical processes and a correlation between morphology and toughness can be established.

H. Beerbaum, W. Grellmann, S. Seidler

B 1.3. Toughness and Relaxation Behaviour of PMMA, PS and PC

Innovative polymer applications which use the specific properties of polymeric materials for selection necessitate, besides the improvement of strength and stiffness, an optimization of toughness behaviour and a well-grounded knowledge of the strength- and toughness-determining mechanisms [1].

W. Grellmann, R. Lach

B 1.4. Crazing in Amorphous Polymers — Formation of Fibrillated Crazes Near the Glass Transition Temperature

Crazing is a widespread phenomenon in polymeric materials. Crazes are zones of highly plastically deformed and highly oriented polymer material, consisting mainly of fibrils along the direction of applied stress interconnected by cross-tie fibrils. The structure of the crazes has been investigated mostly by transmission electron microscopy [1–3] and by X-ray [4] and electron [5] diffraction. The shapes of crazes have been examined by optical methods [6,7]. Various publications review the structure of craze zones in different polymers and the models of craze formation [3,8–10].

G. H. Michler

B 1.5. Influence of Temperature and Moisture on Toughness Behaviour of Polyamide

The thermoplastic polymer polyamide (PA) has a large field of application because of its especially well balanced relation between toughness and stiffness, its good chemical resistance and its uncomplicated processing. However, an important factor in any decision to use polyamide materials is the water absorption, which is influenced by the ratio of methylene to amide groups. The achievable mechanical properties of all polyamide types are strongly influenced by this property.

B. Langer, S. Seidler, W. Grellmann


B 2.1. Relationship Between Fracture Behaviour and Morphology in PE/PP Blends

Inexpensive combined thermoplastics are of great interest for technological application in the marketplace; in particular, blended materials of increased fracture toughness combined with balanced stiffness and strength, as well as appropriate processing and production properties, are highly desirable. At present this goal is reached by methods such as copolymerization or modification with a suitable elastomer.

U. Niebergall, J. Bohse, H. Sturm, S. Seidler, W. Grellmann

B 2.2. Influence of Modifier Content and Temperature on Toughness Behaviour of Polyamide

The modification of polymers for improvement of properties is becoming increasingly important. In particular, polyamide has a wide application field as a construction polymer material. Because of the great variety of possibilities for modification for improvement of the mechanical properties, polyamide is a suitable material for made-to-measure solutions to polymers.

I. Bethge, K. Reincke, S. Seidler, W. Grellmann

B 2.3. Morphology and Toughness of PP/EPR Blends

Polypropylene (PP) is a semicrystalline polymer with a wide range of applications, mainly standard applications but also in the field of construction. The glass transition temperature of about 4 °C limits the use of PP. Compounding with a soft elastomeric phase of a much lower glass transition temperature provides a possibility of expanding the application range of PP to temperatures below 0 °C. The mechanical properties of such blends depend on the structure of the matrix material, on the type, diameter and volume content of the dispersed phase, and on the interaction between the phases. Toughness optimization can only be performed with knowledge of the quantitative correlations between morphology and toughness.

T. Koch, S. Seidler, K. Jung, W. Grellmann

B 2.4. Morphology and Micro-Mechanics of Phase-Separated Polyethylene Blends

A better understanding of the mechanical properties of polymeric materials is a task of particular scientific and economic importance. Because of the large variety of macromolecular and supermolecular structures (the morphology), polymers are inherently capable of large property modifications. The structure or morphology and the mechanical properties are linked by the micro-mechanical processes of deformation and fracture, i.e. by the micro-mechanics [1]. Improved knowledge of the micro-mechanical processes provides a very direct way of improving the mechanical properties of polymers, as shown in Fig. B86.

R. Godehardt, W. Lebek, G. H. Michler


B 3.1. Toughness Optimization of Multi-Phase Polymer Materials Based on a PP Matrix Using Fracture Mechanics Parameters

Besides the development of new materials, the emphasis of international polymer science is on the extension of the range of application of the currently available polymers. Possible ways of achieving this purpose are filling and reinforcing the polymer to increase the strength and stiffness, and the production of blends and copolymers to increase the stiffness, toughness, heat deflection temperature, weathering resistance and environmental-stress-cracking resistance, and to improve the processability. These blends and copolymers consist of a continuous polymer phase and one or several dispersed phases. The dispersed phases may be either polymers or other components. Such materials are summarized in the term ‘multi-phase polymer materials’ [1].

S. Seidler, W. Grellmann

B 3.2. Crack Toughness Behaviour of ABS Materials

It is well known that toughness, defined in the engineering sense as the material resistance against stable and unstable crack propagation or fracture, is a highly important material property. Since excessively small values of toughness often restrict the application fields of polymeric materials, various ways derived from materials science of toughening brittle polymers (for instance SAN) have been developed (such as blending with or without compatibilizer, and copolymerization). This toughening is achieved by heterogenization of the material, i.e. incorporation of fmely dispersed rubber particles into the matrix material [1]. Morphological parameters such as particle size and distance, matrix—particle adhesion, and the internal structure of particles, which vary with production conditions (i.e. synthesis and processing), strongly affect the morphology—toughness correlations since the processes of stable and unstable crack initiation and propagation and of energy dissipation are influenced in different ways.

R. Lach, W. Grellmann, P. Krüger

B 3.3. Fracture Mechanics Characterization of ABS Materials — Influence of Morphology and Temperature

With the growing application field of polymer materials, not only for common but also for technological purposes, the optimization of toughness behaviour, in addition to the improvement of stiffness and strength, has been become a major goal in polymer research [1–4]. The incorporation of a well-dispersed rubber phase into the matrix material has been shown to increase the toughness of glassy amorphous, macroscopically monophase polymers such as SAN or PS that break in an extremely brittle manner [5]. In this connection, ABS materials are an important material group with a broad range of engineering applications [6]. Normally, depending on the particular application, commercial products contain 15–20 wt.% rubber, which corresponds to a balance between toughness, stiffness or strength and price. Depending on the manufacturing process, ABS materials containing rubber particles with an average particle diameter of 0.1–1 μm show the most pronounced influence on toughness behaviour at room temperature (optimum particle size) [7–9]. This observation was verified in [9] by use of a model to estimate the craze volume. Whereas particles with sizes of 0.1–0.5 μm are usually effective in craze initiation, particles < 0.05 μm are not able to initiate crazes [10]. In the case of emulsion-polymerized ABS, the optimum particle size is about 0.3 μm. ABS materials with a multi-modal particle size distribution are often fabricated because other properties besides toughness have a great influence on the overall product quality, for instance hardness, scratch resistance and surface finish. Although ABS materials with broad or multi-modal distributions contain particle fractions that have a lower effectiveness for plastic deformation of the matrix (pp. 335–352), it has been found that their impact resistance is higher than that of materials with narrow distributions [11]. However, the long-time failure behaviour can also be affected negatively (pp. 335–352). ABS materials with a particle diameter of 0.05 μm are scarcely able to dissipate any energy in the impact test, although these materials show a high energy dissipation in the tensile test that is comparable to that of ABS materials with 0.5 μm particles [9].

R. Lach, W. Grellmann, Y. Han, P. Krüger

B 3.4. Brittle Fracture of ABS — Investigation of the Morphology—Failure Relationship

The polymers belonging to the class of acrylonitrile—butadiene—styrene copolymers (ABS) are toughened modifications of styrene—acrylonitrile (SAN) copolymers. The toughening modification is achieved by dispersing submicroscopically small elastomeric particles — mainly derived from butadiene — in the coherent, brittle SAN matrix.

B. Möginger, G. H. Michler, H. C. Ludwig

Hybrid Methods of Polymer Testing and Polymer Diagnostics


C.1. Defect-selective Imaging

Non-destructive inspection of a component means that one has to look for deviations from structural integrity [1]. So there is a need to know what the structure should look like if it were good — and what the real situation is. This comparison can be difficult for complex structures because small deviations may not be obvious. So a method is required which responds only to the characteristic properties of a defect, while it ignores the potentially complicated ‘good’ structure. In this way the non-relevant information is suppressed, while all attention can be focused on the defect.

A. Dillenz, N. Krohn, R. Stößel, G. Busse

C.2. Determination of Local Deformation Behaviour of Polymers by Means of Laser Extensometry

On the one hand, the polymer industry is characterized by an increasing specialization and variety of products. On the other hand, there is also an increasing range of applications for plastics. Chemical and physical modification of the basic polymer materials, often as a result of customers’ demands, has led to a confusing variety of materials on offer. The choice of a specific polymer is often influenced by an insignificant change in the material properties. In addition to such small changes, the cost is decisive in practice.

C. Bierögel, W. Grellmann

C.3. Damage Analysis of Composite Materials by Acoustic-Emission Examination

The damage behaviour of composites is of interest for the purpose of development and application of materials. The strength and lifetime of composite materials are determined by the stress stages of the initiation of micro-failure processes and by the transition of the damage from a subcritical stage to a critical stage. Inter-fibre fracture, delamination and fibre failure are processes of special importance. The damage behaviour of composite materials depends considerably on the crack resistance of the matrix, on the debonding energy of the fibre—matrix interface and, finally, on the delamination resistance of the layers of the composite.

J. Bohse, T. Krietsch

Technological Test Methods


D.1. Polymer-Based Composites for Friction and Wear Applications

Composite materials, one of the most rapidly growing classes of materials, are being used increasingly for technological applications, especially when the tribological behaviour of the material is of interest. The properties of polymer-based materials can be varied and optimized over a wide range with regard to the requirements of the particular application. Some tribological applications, e.g. sliding elements and sliding bearings, require low friction and wear, whereas for other applications, e.g. in clutches and brakes, high friction combined with low wear is necessary (Table Dl). Tribological systems of polymer-based composites against steel are of high interest for technological purposes. Yet much of the present knowledge on the tribological behaviour of polymer-based composite materials, especially high-temperature-resistant (>150 ºC) thermoplastics, is empirical, and very limited predictive capability currently exists. In particular, experimental results of friction and wear tests under conditions close to those occurring practice and basic knowledge of the friction and wear mechanisms in the tribological interphase of polymer materials are needed.

K. Friedrich, P. Reinicke, J. Hoffmann

D.2. Modification of Polymers by Means of Amorphous Carbon for Optimization of Tribological Properties

Heterophasic polymer composites are often used for brake linings. The nature and quantities of the components of the composite have a significant influence on its properties, including, in particular, the tribological properties. Asbestos, which has traditionally been used as an additive to frictional materials, had to be removed from these composites because of its negative influence on human health. As a result, an urgent need arose to develop a new material with properties similar to or even better than those of asbestos. In particular, the new material must ensure an appropriately high level of the friction coefficient and its stability as the temperature rises during brake operation. At the same time, it is necessary to maintain the mechanical characteristics of the brake lining material, particularly its crack resistance. The resistance of the material to microcrack formation and propagation has a decisive influence on the life of facings and thus also on the safety and economy of use of a device.

I. Hyla, J. Myalski, W. Grellmann

D.3. Mechanical Vibration Behaviour of a Compressor Blade Made from a High-Performance Composite

Some components of rotating machines, for example axial-compressor blades, are manufactured from composite materials instead of steel to reduce the weight, with the aim of increasing the throughput (larger blades or a higher revolution rate). Consideration of complex aspects of the transfer of forces into the composite and the mechanical vibration behaviour is necessary before substituting steel by a high-performance composite [1].

W. Grellmann, R. Steiner, I. Kotter, M. Neitzel, M. Maier, K. von Diest

Biocompatible Materials and Medical Prostheses


E.1. Polymer Materials in Joint Surgery

The artificial replacement of joints opened a new era in the treatment of degenerative diseases. It became possible to relieve patients from pain and to give them back nearly normal mobility. Today more than 500 000 prostheses are implanted in the hip joint alone, all over the world every year. With the development of joint replacement during the past 40 years, much research has been done to prolong the survival of joint prostheses and to make them reliable for the rest of the patient’s life. Polymer materials have continued this development; they have become an important constituent part of most prosthesis systems and have prolonged their survival to a range of 12–15 years today. On the other hand, polymers seem to contribute to an aseptic loosening of prostheses after this period, so that they need to be improved further.

J. Brandt, W. Hein

E.2. Material Parameters and ESEM Characterization of Functional ENT Prostheses During Ongoing Degradation

Voice prostheses and tracheal prostheses are functional prostheses that are implanted to copy a natural function. Voice prostheses are implanted in patients who have had their larynx removed for medical reasons. With a voice prosthesis, fast voice rehabilitation is possible. The prosthesis generates the voice only indirectly. It makes possible an airflow that can cause vibrations of the entrance musculature and mucous membrane of the oesophagus. It is a pharyngo-tracheal shunt valve. Because of the overpressure in the trachea, air streams into the oesophagus or the low pharynx area. On the other hand, the passage of saliva and undigested food into the trachea from the oesophagus is prevented because of the valve effect. Perfect valve function is necessary for correct functioning: dysfunction necessitates a prosthesis change. There is a range of products on the market that differ mainly as far as the valve is concerned. The material of choice is silicone rubber. Polyurethane has also been tested as a material. Details of clinical use are given in [1–3].

E.-J. Haberland, A. Berghaus, M. Füting, I. Bethge, W. Grellmann

E.3. Microbial Corrosion of Pharyngo-Tracheal Shunt Valves (‘Voice Prostheses’)

Singer and Blom published in 1980 their technique of the tracheo-oesophageal puncture (T-E puncture), including the application of the first commercially manufactured valve prosthesis. With this method, they started an ever-broadening interest in the voice rehabilitation of patients without a larynx. In the last 20 years different variations of this prosthesis have been developed, which have been tested successfully with several thousand patients [1,2].

I. Šebová, E.-J. Haberland, A. Stiefel

E.4. Deformation Behaviour of Voice Prostheses — Sensitivity of Mechanical Test Methods

Polymer materials are of importance as substitute materials in medicine because their individual properties are specifically adjustable. Their compatibility with the biological system (biocompatibility) and the functionality and stability of the materials used are decisive factors for medical practice, especially for the purposes of implants. The materials commonly used in medicine include PET (textile vascular prostheses), PTFE, PUR (vascular replacements, blood pumps, cardiac valves), polyolefines such as PP or PE (threads, joint replacement), silicone elastomers (prostheses in the ear, nose and throat field, and special orthopaedic items) and polyamide. Pharyngo-tracheal valve prostheses, also referred to as voice prostheses, are used for the rehabilitation of patients who have had their larynx completely removed.

C. Bierögel, I. Bethge, W. Grellmann, E.-J. Haberland

Special Materials


F.1. Crack Initiation, Wear and Molecular Structure of Filled Vulcanized Materials

In their numerous areas of application, elastomer materials are subject to a number of complex wear factors. A typical example of this phenomenon is the abrasion of the tread of a tyre or the pattern of chipping and chunking damage observed under certain circumstances on truck tyre treads [1].

W. Grellmann, G. Heinrich, T. Cäsar

F.2. Investigation of Crack Propagation Behaviour of Unfilled and Filled Vulcanizates

Elastomer materials are used in tyres, conveyor belts, engine bearings and isolation materials, for example. Definite requirements for the material properties depending on application field exist. For tyres, in addition to safety, economic and ecological aspects, wet-skid resistance, rolling resistance and wear resistance are important properties. A predictable lifetime of products is necessary; this is, however, restricted by an inadequate control of wear phenomena.

K. Reincke, R. Lach, W. Grellmann, G. Heinrich

F.3. Characterization of Deformation Behaviour of Modified Polymer Concrete

Polymer concrete is a relatively young material that has been used in the building industry since the 1950s (known then as reactive resin concrete). Since the beginning of the 1980s, polymer concrete has been applied in mechanical engineering. Here, machine bases and components of fast-running machines have been made increasingly of polymer concrete because of its high damping properties for sound and mechanical vibrations and because it is simple to make complicated shapes with it.

H. Wehner, W. Grellmann, T. Hildebrandt

F.4. Fracture Mechanics Testing of Modified Epoxy Resins with Mini-Compact Tension (CT) Specimens

Epoxy resins are used in a wide range of applications. At room temperature crosslinked epoxies typically exhibit a high modulus and a nearly elastic stress—strain behaviour, but they have poor resistance to fracture. Complex material behaviour can often be observed owing to different mechanical and thermal properties (for example, in a sandwich construction), which can impair the overall mechanical—thermal reliability. In these systems, local defects such as cracks can appear as a result of inhomogeneities of the composite material, internal stresses and high thermal and mechanical loading gradients [1–3]. Consequently, the methods of fracture mechanics have an increasing significance regarding the assessment of the failure behaviour. The aim is an optimization of the toughness of epoxies under extreme conditions. Concerning the dimensioning, geometry-independent parameters have to be used in order to guarantee optimum reliability and operational safety in industrial applications (pp. 3–26). The usual compact tension specimens require a large amount of material and are often unsuitable for experimental investigations. In the future, the application of miniature specimens for the determination of fracture mechanics parameters should be made possible so that an efficient toughness evaluation of newly developed materials can be performed [4].

H. Walter, C. Bierögel, W. Grellmann, M. Fedtke, B. Michel

Examples and Limits of Application


G.1. Modelling of the Mechanical Behaviour of Non-Linear Viscoelastic Materials under a Multi-Dimensional State of Stress

The mechanical behaviour of non-linear viscoelastic materials depends on the time, the temperature, the loading rate and the magnitude of the load. The aim of the work described in this chapter was an investigation of the effect of a biaxial state of stress on the characteristic functions, such as the secant modulus versus strain. A model is presented that allows the simulation of non-linear viscoelastic materials under a multi-dimensional state of stress.Therefore, a suitable test specimen and testing machine were developed. Because the specimen is produced by injection moulding, both isotropic and anisotropic specimens can be produced. The testing machine enables strain- and force controlled experiments. Uniaxial quasi-static strain-controlled experiments on test specimens made from polyamide 6 (PA 6) and from a styrene-butadiene-styrene (SBS) block copolymer demonstrate the effect of the process parameters on the mechanical anisotropy. As far as the isotropic PA 6 is concerned, approaches based on energy absorption and equivalent stresses show the possible ways to transform the secant modulus from a uniaxial to a biaxial state of stress in the case of quasi-static loads. Dynamic experiments demonstrate that the load history must be taken into account when considering multi-dimensional states of stress. The approach mentioned above cannot achieve this. Therefore, a three-dimensional model has been developed to simulate multi-dimensional load histories. This three-dimensional deformation model is based upon the uniaxial deformation model and is constructed from a parallel arrangement of a certain number of basic elements. Each basic element consists of an elastic Hookean element and a damper system (3D damper) to describe the viscous properties. The arrangement is calibrated by means of isothermal strain-controlled tensile tests at different temperatures. Along with suitable calculation algorithms (relaxation algorithm and retardation algorithm), this model offers the ability to simulate any multi-dimensional load history caused by direct stresses. The model allows the simulation of both quasi-static and dynamic loading at different temperatures. By comparing the experimentally determined static and dynamic stress-strain curves with simulated curves, the suitability of the model developed here is demonstrated. Relaxation effects are overpredicted by the mode L in comparison with experimental results. Better calibration should lead to an improved correspondence.The aim of further investigations should be the expansion of this model to thermal stresses and, later, implementation in finite-element programs.

E. Schmachtenberg, M. Wanders, N. M. Yazici

G.2. Detergent Resistance of PP/GF Composites

The increasing requirements for lightweight construction are leading to a wider acceptance of alternative materials for purposes where metals have traditionally been used. As a result of new technologies, these materials are being used for the substitution of conventional materials in components and structures. Polymer materials are fording increasing application in components subject to thermal and detergent loading. At present, thermoplastics based on mass-produced polymers are favoured because of their well-known advantages of properties, processing and price. The reservations about the use of these materials are due to a lack of knowl-edge about the parameters relevant to structural use and the lack of reliable morphology—property correlations.

W. Grellmann, S. Seidler, C. Bierögel, R. Bischoff

G.3. Material Optimization of Polypropylene—Short-Glass-Fibre Composites

The adaptation of material characteristics to specific applications by using different fillers and reinforcements and/or using composite materials is an international trend in the development of the properties of polymers. A necessary condition for specific requirements on the strength and toughness level of polymers to be satisfied is a knowledge of the deformation and fracture mechanisms [1,2].

B. Langer, C. Bierögel, W. Grellmann, J. Fiebig, G. Aumayr

G.4. Influence of Exposure on the Impact Behaviour of Glass-Fibre-Reinforced Polymer Composites

Glass-fibre-reinforced composites based on thermosets show good mechanical properties, such as high specific strength and stiffness, combined with an excellent chemical resistance. An increasing use of such materials in a wide range of engineering applications and structures, especially as lining materials for containers and pipelines, can be observed. In recent years, many research programmes have been studied the mechanical properties of composites. However, independently of these investigations, reservations about the application of composite materials in the chemical industry exist because exact criteria for lifetime, chemical resistance and moisture ageing are not or are rarely available. Additionally, the evaluation of the damage state of a composite, as well as of the functionality, reliability and impact behaviour, is complicated. A successful failure analysis of structures made from composites depends strongly on suitable non-destructive test and inspection methods.

H. Walter, C. Bierögel, W. Grellmann, B. Rufke

G.5. Physical Ageing and Post-Crystallization of Polypropylene

Among thermoplastic polymers, polypropylene (PP) is one of the most rapidly developing product families owing to its property profile, the range of possible modifications and its excellent environmental record [1]. Associated with this development are a quantitative growth well above the average and a continuous expansion of its application areas. Technological applications demand tailor-made PP systems with an optimized adjustment of polymer design, processability and properties in the final application. Here, it is often assumed that the properties of a moulded component remain constant for its whole lifetime — even if the producers and processors of PP are well aware that the properties of polymers change continuously over a very long period of time and even if the producers and processors take account of this fact, e.g. by fixing the time between processing and standardized testing.

J. Fiebig, M. Gahleitner


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