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Proceedings of the 5th International Conference on Integrity-Reliability-Failure, Porto/Portugal 24-28 July 2016

Editors J.F. Silva Gomes and S.A. Meguid

Publ. INEGI/FEUP (2016)

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PAPER REF: 6306

THE PREDICTION OF FRACTURE TOUGHNESS PROPERTIES

OF BIOCERAMIC MATERIALS BY CRACK GROWTH

SIMULATION USING FINITE ELEMENT METHOD

AND MORPHOLOGICAL ANALYSIS

Dariush Firouzi, Amirsalar Khandan(*), Neriman Ozada

Mech. Eng. Dept., Eastern Mediterranean University, North Cyprus, Gazimağusa, TRNC, Mersin, Turkey (*)

Email: [email protected]

ABSTRACT

Various types of hydroxyapatite (HA) structures have received great attention of scientific

researcher in biomaterials field. Also, it is common that HA is the essential inorganic

materials in human hard tissue such as bone or teeth. Fracture toughness and micro-hardness

properties are the important parameters required for the prediction of the mechanical

performance of biomaterials structures before failures. The indentation micro-fracture

method, which yields for the mode is critical stress intensity factor, KIC, is particularly useful

when applied to brittle materials with low KIC. As fracture toughness is easy, fast technique

and needs small testing equipments and area, here we represent the enhancement in hardness

and toughness which is possible due to attain nano-crystalline size for HA powder using in

powder, bulk or coating form, suitable sintering and variable composition. It is obvious that

the HA hardness have close relationship with fracture toughness. Also, materials properties as

the size of grain changes/reduced from micron to nano-meters influence the mechanical

behaviour of biomaterials. As the current observation of papers illustrates, the HA toughness

rise up to about 70% with compositing with other beneficial additives like Al2O3,

polyethylene, fluorine, diopside, zircon, akermanite, bioglass (BG), tungsten carbide (WC),

carbon nanotube (NC), etc. Secondly, sintering improve the fracture toughness of the HA

particles and other biomaterials as well. Also, one can say that sintering procedure effect the

microstructure mechanisms for simultaneous enhancements in the hardness and fracture

toughness of the bio-ceramics. In the current paper we predict the fracture toughness value

changes to greater value with the morphology of the powder less in the case of amorphous

materials like zircon. We consider the prediction method with Finite element analysis and

gather data from other literatures.

Keywords: Fracture toughness, sintered, non-sintered, powder, bulk, coating, biomaterials.

INTRODUCTION

The aim with the current paper was studying several literature regarding to fracture mechanics

relates to the mechanism of products, geometry of materials, load application of bio-ceramics.

It has been well recognized that bio-ceramics like hydroxyapatite (HA) is the basic inorganic

materials human bone structure [1]. Research observation on in vitro test represented, it has

the natural capacity to advance bone development [2]. Biomedical applications of bio-ceramic

as well as in artificial bones implant are recently being clinically investigated. Various

procedures (sintering, grain size, composition) have been examined in endeavors to enhance

Symposium_12: New Materials and Design Processes in Dental Medicine

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the mechanical properties for coating case and other specific applications [3-4]. This ability

can be further improved by arranging of additive (various ions) into HA structure gradually

by the encompassing bone showing cells which produced novel structured product [4]. As the

second materials (phase) added to advanced biomaterial structure, other properties like

mechanical behaviour like fracture toughness, micro-hardness, and thermal behaviour could

be enhanced due to different synthesis technique and materials fabrications methods like

mechanical activation (MA) [3, 7, 15], mechanochemical (MC) [4], sol-gel, precipitation, etc

[4-6]. Strength properties of Ca10(PO4)6(OH)2 have been well investigated in several literature

[6-10]. Because pure HA is very brittle compared to other ceramic, which is enough strong

under compression test, however the materials properties is weak under tensile examination,

micro hardness and shear stresses sample test [9]. However, high applications have been

encountered with some limitation to non-load-bearing conditions because of its low

mechanical properties, high dissolution rate and particularly low fracture toughness (low KIC)

[11-12]. In this literature, we investigate fracture toughness of HA in the form of powder

composite and bulk dense materials. We present the materials and techniques that are possible

to upgrade and improve these types of unique materials. Many experimental methods have

been proposed to estimate roughness and fracture toughness of the coatings [12-13]. The

fracture toughness of HA is less than KIC<1 MPa m1/2

which is a principle disadvantage of

this materials limits for bearing orthopaedic and clinical applications [14]. The indentation

micro-fracture method, which yields for the different three mode like tensile force (mode-I),

shear force (mode-II), and torsional force (mode-III) is critical stress intensity parameter, KIC.

It is particularly useful when applied to brittle materials with low KIC. In addition, the

biological evaluation of bio-ceramic shows that in vitro and in vivo studies have close

correlation with fracture toughness as mechanical behaviour [15]. Bioactivity and

biocompatibility evaluation supporting a human cell reaction on synthesized materials and

results showed that composites demonstrated no deleterious defect on some antigen

expressions that play a vital role in the integrity fracture toughness (KIC) was determined by

an indentation technique as proposed by Laugier [16] and Evans [17]. The densification

behaviour and mechanical properties of sintered and non-sintered HA effects on biological

reaction as the several literature review illustrates [18-21]. As the HA biocompability and

bioactivity proves with several characterization technique like cell culture and simulated body

fluid (SBF) solution test, the mechanical characterization of HA is still a interesting topic in

the recent years [9, 12]. Applying of calcium phosphates (CaPs) as artificial organ in human’s

body has been constrained by low quality and low crack durability in the implant coating

using in dental and orthopaedic prosthesis [3]. Furthermore, nanostructured bredigite

(Ca7MgSi4O16) [22], fluorine [4], nanostructured diopside (CaMgSi2O6) [3, 9], poly

caprolactone, nanostructured akermanite (Ca2MgSi2O7) [1-3], polyethylene, Al2O3, and

tungsten carbide (WC), have discharge at a controlled rate to strength the HA arrangement for

better mechanical reaction/behaviour. The crack durability and KIC for tungsten carbide (WC)

is 6 MPa m1/2

is accomplished with the SPS procedure. Additionally, some polymers like

poly-imides have been composited and sintered to enhanced mechanical properties of primary

and pure material [3]. Their outcomes also demonstrated that the mechanical and biological

properties of the composites were better than those delivered by cold isostatic pressing (CIP)

and conventional sintering. In every case study with proper fracture toughness, mechanical

properties were observed that enhanced by compositions and sintering [6, 17]. Another factor

which influence the fracture toughness of HA materials is the term of temperature which

changes in higher heat condition between 800-1300°C for different biomaterials [1-3].

Applying these parameters like sintering, change in morphology, grain size, composition

allows the HA to be utilize for suitable artificial organs under high load bearing situation [3,

Proceedings of the 5th International Conference on Integrity-Reliability-Failure

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12]. Here we illustrate a valuable reference data to predict enhanced mechanical blends of HA

at high temperatures with different particle size. Such composites plan to hold their valuable

bioactive properties whilst giving more suitable mechanical properties to specific

applications. In addition, the improved fracture toughness is connected with the

microstructure of the compacts. The objective of the current report was to investigate the

fracture toughness HA-added with some reinforcement and different sintering temperature

and condition.

EXPERIMENTAL PROCEDURE (FRACTURE TOUGHNESS)

Fracture toughness (KIC) play a vital role in the integrity mechanical reaction was determined

by an indentation technique as proposed by Laugier and Evans [16] as following Eq. 1.

KIC = 0.015(�� )(

��)2/3 �

√�� Eq. (1)

Where c is the crack length, a, the half of the diagonal indention, E, the Young’s modulus, H,

the hardness, P, the load applied and y is a polynomial function ofca. A standout amongst the

most imperative controlling parameter that must be considered amid the preparing of

hydroxyapatite is the determination of suitable powder solidification/sintering system to get a

strong, high thickness HA body that is portrayed by having fine microstructure. The most

ordinarily utilized union strategy is the traditional sintering technique. In any case, this

strategy frequently requires long sintering calendar, ordinarily above 18–24 h which thus

bring about coarse-grained microstructure and low mechanical properties. Thus, a more quick

method, for example, microwave handling has been accounted for to create a thick sintered

HA body that had fine microstructure combined with enhanced mechanical attributes.

Sintering by microwave since heat is created inside of the material as opposed to being

transmitted from outside the body as in routine sintering. The goal of the present work was to

contemplate the impact of sintering on the densification and mechanical properties (fracture

toughness) of nanocrystalline HA powder, bulk and coating arranged through a synthetic

methodology.

Effect of sintering of ceramics (Fracture Toughness)

Densification and mechanical properties of biomaterials that mixed showed a quick decrease

in the crystallite size and improve the strength as shown in ref [3]. The decrease in crystallite

size and synchronize strong arrangement of particles in the structure is obtained by suitable

sintering system. At lower surface region for the powder may have been various charges

phase transformation, the higher surface region for biomaterials powder my influence on

lower mechanical and chemical stability of element [1-3]. Densification amid sintering is

managed by mass exchange through instruments, for example, evaporation–condensation,

surface dispersion, volume dissemination and grain limit dissemination [1, 4].

Finite element analysis (FEA)

Applying finite element analysis to investigate distribution of stress in the contact area is

useful technique. This comparison reveals that the shear testing consequences with the FEA

records have a close correlation between the failure patterns and the stress distribution

identified by the FEA [23].


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Fig. 1 - Both the three point bending (1) test specimens (3×3×22 mm

3) and the symmetrical biomaterial (2) test

specimens (2×6×20 mm3) were tested at a load rate of 1mm/min [23]

In the work presented by other researchers with FEA study, a case study was conducted with

an experimental work, Toparli and Aksoy [23] discover the validity of the fracture toughness

and adhesive bond toughness of composite made of dentin-resin interfaces from a fracture

mechanics standpoint [figure 1 (1-2)]. The result of the work deal with fracture toughness

(KIC) and fracture energy (JIC) range of two different composite by using single edge notch

(SEN) specimens loaded in three point bending (Fig. 1-1). The result indicated the fracture

loads in tension of bonded composite–dentin specimens (Fig. 1-2). The result for their work

was not trustable for KIC values with the bonded samples, due to the crack occurred at

interface of part [23].

Fig. 2 - Concentration of stress in at elliptical defect, a=3b in Cartesian coordinate system [23].

According to the Inglis’ report [23] stress analyses of elliptical defects reveal their impact

(Fig. 2). The ơxx stress which is perpendicular to ơyy, increase from zero to a sharp peak

within a small distance from the flaw tip and subsequently drops toward zero with the same

tendency as ơyy as shown in figure 1 [23].


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Definition of fracture energy and toughness

Fracture energy (G) and fracture toughness (KIC) are defined as important parameters which

represent a fundamental introduction in fracture mechanics researches. A report released by

Griffith [23] presented that KIC happens as enough mechanical energy is released from a

stress field, type of energy that is required to create a fracture surface in the propagate of

crack. This type of energy which released received from potential energy of the loading

system. Recent work by Irwin declares that the stress field in the sharp crack in a linear-

elastic material could be uniquely defined by a parameter named the stress intensity factor, K

[23]. According to Inglis’ analysis, the level of these stresses near to an elliptical crack in a

bulk material (in tension) can be written as following:

σij=σ0(a2r)

1/2fij(θ) Eq. (2)

where σij is the parts of the stress tensor at a certain area, ij, σ0 is the total level of applied

stress, r and θ the polar coordinates of point i and j using the crack tip as the origin,

and a shows half the length of the crack (��

� � �). These modified equations by

Irwin are represented like equation 3:

σij=K

√�2πr)) fij(θ) Eq. (3)

Where K was represent as stress intensity factor. K relates to the magnitude of the stress

intensity locally adjacent to the crack tip in terms of the applied loading and depends on crack

geometry where it placed. As a result, for a crack occurred in the central region, above two

equations can be mixed into one following equation 4:

σ0 �� fij (θ)=

K√2πr fij(θ) or K=σ0(aπ)

1/2 Eq. (4)

where K = σ0(aπ)1/2

shows the fracture toughness of central crack. The following situation is

connected with tension of the sample. Although, three various types of load conditions are

available which leads to the initiate the cracks or propagate. The various three load conditions

are denoted modes-I, -II and -III as shown in figure 3.

Fig. 3 - Failure modes in three load conditions. (A) Tensile force shows in mode-I, (B) Shows shear force mode-

II, and (C) Shows torsional force mode-III [23].

Also, one can say, crack propagates with three different load conditions denoted modes-I, -II

and –III (Fig. 3) [23].


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Mechanical characteristic of sintered materials

The sintered compacts created in authors work display a more noteworthy thickness and littler

grain size than different reports [20]. It may be credited to processing of the calcined

materials in ethanol which is isolates the crystallites and avoids agglomeration that generally

happens because of the hygroscopic way of HA particles. The little size of grain extent in the

sintered compacts recommends little impact on microhardness [9]. By considering the

decreasing fractures toughness of mentioned is due to amorphous properties of zircon and it

structured. In the case of when 15 wt% zircon was added to the HA under the same condition,

the KIC average became 91 MPa. Difference is proper result in to find with the vicinity of the

ZrO2–Al2O3 crystals safeguarded in the HA framework. As more increment in the containing

of Zr powders, both the twisting quality and the crack strength disappeared. As the zircon

increase into composite it shows that porosity starts to be increased. To solve this issue Al2O3

can be added to ZrO2 to decrease its negative results and improve the fracture toughness.

Along these lines, Al2O3 and ZrO2 both influence quality and strength of HA composite.

The compositional, thermal, mechanical and properties of HA/phosphate glass composites are

connected with structural behaviour of particles which can be determined by various

techniques like BET, PSA, SEM instruments [21]. As the reviews shows fabrication of

composites bio-ceramics glass increases the mechanical behaviour of product with

simultaneous enhancements in hardness and toughness within 10 wt.% to the best potential

average because of their close compositional similar to osseoconductive and reaction of

biomaterials.

Toughness of sintered HA bodies

The toughness result for sintered HA is represented that toughness has close relation with

crystal diameter. The graph introduced that the HA toughness rise up, as the grain size of the

materials decreased. The data shows the indentation toughness for the sample sintered at the

850°C have a grain size about 67 nm and toughness of 1.06 ±0.16 MPa m1/2

which is 73.8%

higher than the indentation toughness (0.61±0.04 MPam1/2

) of the 1200 °C-sintered HA with

an average grain size of 732 nm. Moreover, most of the toughness increase takes place in the

range of grain sizes smaller than 141 nm above which the toughness appears to be

independent of grain sizes. Reviewing substitution fluorine into HA show that manufactured

FHA have improved structured for mechanical reaction like fracture toughness. The

methodology used for the producing FHA and these types of CaPs is really influence the

mechanical powder of powders. Constrained data on the impact of fluoride substitution for

HA shows an improved the mechanical properties of HA in mechanical behaviour by adding

second phase to HA. Crack durability is enhanced with fluorine consolidation into the cross

section and achieves a crest of 1.8 for a 95% thick sintered pellet with a 60% fluoride

substitution, trailed by a quick abatement at higher fluoride fixations [4]. High fluoride levels

are unfavorable from a mechanical point of view, are not suggested for biomaterials, and can

prompt a higher frequency of break where sodium fluorine, for treatment of osteoporosis, may

create an exceptionally FHA [4].

Impact of sintering temperature

The impact of sintering temperature of incorporated nanocrystalline HA was researched. The

beginning powder was incorporated by means of a novel wet substance course [1-4]. HA

compacts were arranged and sintered in climatic situation at different temperatures running

from 900–1300°C. The outcomes reveals that fracture toughness reaches to 1.17MPa m1/2

and


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Young's modulus of above 110 GPa were acquired for HA sintered at temperature as low as

1050°C. According the fact that the Young's modulus expanded with expanding mass

thickness, the hardness and crack fracture of the sintered material began to decay when the

temperature was increase from 1000–1050°C in spite of displaying high densities 498% of

hypothetical quality.

Sintering or non- sintering

Although several recent studies show that there is a possible improvement in the hardness and

toughness of HA with decreasing the grain size, but in some cases researchers illustrate some

other result which is in contrast with the previous research or some other report there is no

changes [3].

Table 1 - Changing of fracture toughness at different temperature and value of hardness and fracture toughness

of biomaterials in various research papers [1-4, 8-9, 20].

Powder type Temperature (°C) Young’s

Modulus (GPa)

Hardness Fracture Toughness

(MPa m1/2)

Ref.

Sintered Conventional

HA 1100 87±4 508±40HV 0.77±0.12 [8],[9]

HA+CaPO4+ZrO2 1100 130±6 5.5±0.5 GPa 1.60±0.21 [2] HA+CaPO4 1100 103±9 5.7±0.3 GPa 1.17±0.11 --

HA 850 47 110 0.6-1 [1, 3] Diopside 1350 170 300 1.8-2.4 [9]

Dense Bone -- -- -- 2-12 [20] sponge Bone -- -- -- Not observed [20] Magnesium -- 41-45 GPa -- 15-40 [22] Dentin -- -- 1.0–4.0

Ti-6Al-4V -- 110-117 -- 55-115 [3] Co-Cr alloy -- 230 -- N/A [3] Stainless steel -- 189-205 -- 50-200 [2] HA+CaP+ZrO2 1100 108±4 5.2±0.2 GPa 1.41±0.11 [2]

Reported analysis that considers the sintering process in various temperatures (900 °C and

1200°C) for HA. It is obvious that at 900°C fewer cracks propagate and have a higher crack

growth resistance more than the sample sintered at 1200°C. The reason for this phenomenon

is the crack with a shorter length is created at 900°C-sintered HA [3-5].

RESULTS

Geometry of as-splashed powders and sintered

Fig. 4 demonstrates the surface morphology of the as-splashed particles. It is apparent that the

particles are almost circular fit as a fiddle and the diopside particles (brilliant dabs) are

consistently disseminated in the CaPs grid all through the volume of the powder particles.

Fracture toughness

HA looks to be an important bio-ceramic for biomaterials application like dentin and bones

with proper biological behaviour. However the mechanical behaviour of HA in pure form is

weak and not able to have excellent fracture toughness (KIC) more than 1.0 MPA m1/2

compared with authentic bone which is 2-12 MPa m1/2

. The application of these types of

powders, coatings, and low-loaded porous implants are not enough strong. Due to improve

the properties of HA ceramics, various reinforcements and additives have been developed

(ceramic, metallic, or polymer). Pure HA and dense HA ceramics has KIC in the range


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amount of 0.8–1.2 MPa m1/2

with an average of 1.0 MPa m1/2

. As the porosity increases the

KIC begins to decrease linearly.

A case study performed in powder sample

A case study is performed in our previous works including powder preparation [1], coating

[2-3], bulk materials [4]. Fatty calf bones are bought; the bones are boiled with hot water for

several hours. The boiled bones were heated with direct heat. The result of heated bones

(black ash) is milled with milling process to reach pure and homogeneous powder. The

outcome is black bone ash was heated for 3 h at 750°C, 850°C and 950°C, Figure 4.

Fig. 4 - Effect of sintering on the powder sample with various in HA microstructure heated for 3 h at 850 °C and

composited with diopside powder

Table 2 - Values crystallite size average at any given heat treatment [1].

Sintering heat (°°°°C) and time (h) Length of particle (nm)

750 for 3 29

850 for 3 43

950 for 3 51

850 for 2 33

850 for 1 34

XRD patterns in figure 6 show a gradual sharpness peaks when the temperature increases, that

showing the crystal grow of HAs. Relatively gradual decrease in β. Cosθ and almost increase

in L values )./.( θβ CosconstL = is observed with the increase of 2θ. This is equivalent toLKCos /ln)/1(ln8149.4ln λθβ += . It is interesting to notice that although variations exist in lnβ

values, but the intercept systematically changes as -5.1196, -5.5542, -5.6054 and -5.6276

respectively for 600, 700, 900 and 1100°C [1-4]. The result of temperature versus length of

the particle is represented in table 3 [1, 2].

Table 3 - Treatment of linear plots to obtain nano size of crystallites [1-3].

Temp (°°°°C) L

k

e

λln

L (nm)

750 006.01196.5 =−e 24

800 00387.05542.5 =−e 36

850 00368.06054.5 =−e 38

1000 0036.016276.5 =−e 39


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A case study performed in coated sample

As the case of coated samples consideration to discover implant coating effect with EPD or

plasma spray technique and effect of voltage on the surface modification, also a case study is

conducted in which the specimen with different percentages of diopside (as a second phase)

synthesized with mechanical activation process. The observation of were done by considering

the cross section of scan electron microscopy (SEM) images after sintering the coated sample

at 850°C. The results illustrate that sample which is coated with 50V were crack free although

the sample with 40 V has a great crack (Figure 5) due to improper voltage and heavy particles

in the ceramic solution [3, 9]. Data after this observation gathered and a clear results show

that the optimum values for temperature are is 850°C in order to have surface without crack.

The SEM micrograph reveals that particle size of the materials has a close correlation with

temperature (sintering) which creating a crack in the coated sample [3]. It is obvious that with

particles with the size of less than 1 µm have proper distribution in the ceramic solution for

the sample composed of 30 wt% Di powder that has coated on the Ti alloy [3, 9].

Fig. 5 - Effect of sintering on the coated sample with various % of diopside in HA microstructure

in the paper published in ceramic international journal [1-3].

As mentioned above the maximum range for KIC is dedicated to fibers made of ceramic

reinforced HA. However, there are several problems happened to coat ceramic powder to

metallic implants, because of wear corrosion and other negative reaction. Most of the dental

and orthopaedic implants are encapsulated by hard fibrous tissue which avoid suitable

changes in stresses distribution and became one of implant loosening reason [3-6]. Also, the

vicinity of β-TCP with KIC = 1.3 MPa m1/2

become more strong than HA, and would have

been supporting to enhancing the typical fracture toughness. As the literature by other authors

indicates little amount of bioactive glass (BG) are mixed to HA powder leads to enhance the

solidification and improved the fracture toughness for pure HA. KIC factor for bio-ceramics is

a certain amount with minimum of 1.0-1.7 MPa m1/2

. In some case, as the fracture toughness

increases the strength has been increases. Typically, addition of BG powder enhances

decomposition of HA in great percentages. Nanocomposite HA with polyethylene additive

show brittle/ductile transition at a HA volume content of about 40–45% [8]. Compared with

cortical bone these nanobio-composites have shown an excellent KIC for HA lower than 40%

and same KIC in the range of 45–50%. Young’s modulus of these types of additives is in the

range of 1–8 GPa, which is quite close to the Young’s modulus of bone. However, such

additive like polyethylene’s which reinforced HA are not biodegradable [8]. Moreover, the

presence of bio-inert polyethylene decreases the ability to bond to the bone [8]. Also, other

drawback is for coated metals implant with polyethylenes and load-bearing approaches in


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comparison with polymeric biomaterials causes to their adding of higher strength and KIC.

These days, it is recommended for bio-metallic such as stainless steels (SS-316 L), titanium

(Ti-6Al-4V) and cobalt–chromium-based alloys to coat with these types of bio-ceramic with

high fracture toughness properties. However, these bio-metallic have some problem like

possible release of toxic metallic ions and subsequently wear resistance and negative

corrosion which may influence to solve by coating. To summarize the influence of

composition and sintering on fracture toughness of HA structure, it is shown that the

toughness and durability of the sintered HA at 1200°C is close to the other researcher reports

by various agents for high sintered HA is about 0.6 MPa m1/2

and sintered HA fracture

toughness about ≤ 0.73 MPa m1/2

. Reports indicated that process of spark plasma sintering

(SPS) of HA is about 1.0–1.4 MPa m1/2

[20] and 1.15–1.25 MPa m1/2

. A similar pattern is

discovered, that shows correlations between SPS process and higher strength of materials

especially fracture toughness more than other technique like conventional sintering and hot

pressing sintering. The grain size average of materials starts to decrease to 50 nm for HA and

leads to KIC 1.52 MPa m1/2

. These averages reach us to the conclusion that the strength of HA

increments with diminishing grain size in the nano-meter range is higher.

CONCLUSION

Biomaterial fracture toughness behaviour

To understand better definition of fracture toughness the following aspect should be

considered:

� Local stress and growth of crack occurred as a fracture toughness in the case of

fracture mechanics. Also, one can say a part does not damage or ruin instantaneously; it

destroys as a local area start to create a crack and propagate.

� Basic description of fracture mechanics describes that internal properties of

biomaterials like porosity, Gc, Kc can be measured and evaluate to discover different materials

reaction. From these parameters is correlate with thermodynamic approach.

� Several modes of failure are happens in fracture mechanics of materials.

� When the crack propagates in near to an interface, the various failure modes

can contribute to crack propagation.

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