Summary of all the content, including the lectures, for the course introduction to building physics and material science for first-year students studying architecture, urbanism, and building sciences at the TU Eindhoven
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7S3X0 – Introduction to building physics and material science
Reader: Application of materials in the
built environment
Chapter 1: Building material properties
1.1 mechanical properties
According to their applications, materials are often subject to different forces or loads when they are
used. The applied force can be measured as well as the resulting deformation of the material under
this force.
Material scientists have designed standardized tests to learn about different material characteristics
that we call mechanical properties.
1.2 stress/strain relations
In order to measure mechanical properties, different methods can be used. Tensile testing is the most
common test on which we base the characteristics of materials.
𝐹𝐹
Stress is a force divided by the area, this we note by the following: 𝜎𝜎 = in which So = cross-section
𝑆𝑆0
of the round sample.
To study specimens with different length, elongation of the tested material should be relative to its
∆𝐿𝐿
initial value. This we call the strain: 𝜀𝜀 =
𝐿𝐿0
A tensile test records the stress as a function of strain. Several points are essential to know on this
curve as they characterize important mechanical properties. Three of those are explained in a stress-
strain curve below.
1 = Yield strength, it defines the stress at which the tested material
begins to deform plastically and terminating the elastic deformation.
2 = Ultimate tensile strength, it defines the maximum stress that a
material can undergo before failure.
3 = Strength at failure, it defines the stress when the material eventually
breaks.
The yield strength can be sudden or progressive when the transition of a material is very aggressive.
This makes it difficult to measure the exact value of the strength, therefore a 0.2% deformation limit
is included in the calculations.
Do not mistake the elastic deformation with the plastic deformation. The elastic deformation is
reversible and can be measured in the linear part of the curve while plastic deformation is irreversible
and occurs after the theoretical yield strength.
Lenore van Vliet - 1377892
, 7S3X0 – Introduction to building physics and material science
1.3 Main mechanical properties
Mechanical properties can either be intrinsic or extrinsic, an intrinsic property means that it only
depends on the atomic structure of the material. Likewise, the extrinsic property is one that depends
on a lot of external factors.
1.4 Stiffness
The stiffness is defined by the relation between the load and the material’s deformation. It is
represented by the elastic modulus, we define it as young’s modulus (E). Young’s modulus can be
calculated by using Hooke’s law: 𝐸𝐸 = 𝜀𝜀 × 𝜎𝜎
Hooke’s law is linear since the equation shows a direct and proportional relationship between stress
and strain. Therefore on a stress-strength curve, the linear part of the curve starting from the origin
and finishing at the yield strength correspond to the validity area of Hooke’s law.
The stiffness of a material is an intrinsic property. It means that the
shape or the surface appearance of the specimen has no impact on the
value for E, the young’s modulus of a material is set as a universal value
which can be found in tables. It can be explained by the fact that the
stiffness of a material is defined by its atomic structure and the type of
chemical bonds between atoms.
Chemical bonds
We currently know of four different bonds between atoms:
Ionic and covalent bonds are the strongest since a lot of energy is required to break them.
Metallic bonds can be either really strong or relatively weak depending on the electrostatic attractive
forces between conduction electrons.
Intermolecular bonds are weak and purely represent the forces between molecules.
Spring theory
The stiffness of a material is directly connected to the strength of its bond. The spring theory explains
this: when a force is applied to a material, the chemical bonds act as a spring where the spring
constant depends on the bond’s strength. There are two formula’s that are used to calculate the force
𝐹𝐹 𝐿𝐿0 −𝐿𝐿𝑓𝑓
and the cross-sectional area:𝐹𝐹 = 𝑘𝑘 ∙ �𝐿𝐿0 − 𝐿𝐿𝑓𝑓 � or = 𝐸𝐸 ∙
𝑆𝑆0 𝐿𝐿𝑜𝑜
Lenore van Vliet - 1377892
, 7S3X0 – Introduction to building physics and material science
Strength and stiffness are often mistaken while stiff materials are often strong which is not always the
case.
1.5 Brittleness and ductility
The brittleness is often defined by spontaneous breaking of the material when no visual deformation
is shown before failure as the material only undergoes elastic deformation.
In non-brittle fracturing materials, increases in tensile stress lead to plastic deformation instead of
sudden fracture. As the load increases, we can visually become aware of the existing atomic bonds
being destroyed and get replaced by other new atomic bonds
A ductile material can be brittle depending on the conditions, one of which is temperature. When a
material can shatter on impact when it is extremely cold a phenomenon called ductile-brittle
transition temperature can occur.
Ductility of metals
Most metals are crystalline, meaning that they are organized in grids where the metallic atoms are
ordered precisely along the axis, but in any crystalline structure imperfections can be found. These
imperfections can be a point defect, vacancy, a line defect or a planar defect.
Line defects or dislocations explain the ductility of materials. When a metal is exposed to stress higher
than its yield stress, the energy stored inside the material is high enough to break the bonds between
metallic atoms. The energy they need to move a dislocation is less than the energy required to
fracture the material.
The number of dislocations per unit volume is the dislocation density.
At high temperatures (e.g. when a fire occurs) metallic bonds do no longer function properly and a
metal will soften and eventually melt.
Hardening mechanisms in metals
Imperfections in atomic grids make possible the strengthening of metals by incorporating a low
fraction of foreign atoms. The dislocation diffusion decreases as the ratio of foreign atoms increases.
Ductility polymers
Polymers, especially thermoplastics and elastomers are known for their low stiffness but their
extraordinary ductility. A polymer is considered as a macromolecule where a small repetitive unit
reacts to form numerous long carbon-based chains.
It is fairly common to find amorphous and crystalline phases in semi-crystalline polymers. The
crystallinity of a polymer depends on the cooling rate at which the polymer is formed: a slow cooling
process allows the polymer chains to be ordered whereas a fast cooling rate does not.
Thermoset polymers are always amorphous since they are networked and cannot be ordered
accordingly.
Lenore van Vliet - 1377892
, 7S3X0 – Introduction to building physics and material science
A = two separate polymer chains
B = branched polymer or a thermoplastic polymer
C = cross-linked polymer or an elastomer
D = network polymer or a thermoset polymer
The polymer chain is constituted of strong covalent
bonds but interactions between chains consist of weak
intermolecular bonds. When the polymer is stretched
these weak bonds are broken causing a decrease in
entropy of the material.
Because of the very short range of temperature in which polymers behave normally, using polymers as
essential parts of a load-bearing building structure is incorrect and also legally forbidden.
1.6 Strength
The strength of a material is represented by its ultimate tensile strength (UTS). It defines the
maximum occurring stress tolerated by the material before failure. The plastic deformation increases
after the stress decrease, due to the constriction of the section since measured stress decreases while
the material section decreases, this is called necking.
Unlike stiffness, the strength of a material is not an intrinsic property. It is for this reason that yield
strength and UTS are given as a range of values.
Ceramics do not have plastic deformation hence the yield strength is always the same as the ultimate
tensile strength.
Stress concentration
In material science, defects or geometric discontinuities are called stress concentration or stress riser.
The crack propagation initiated by a stress concentration can lead to material failures below its
theoretical strength. This mainly happens with brittle materials. The local stress is calculated using:
𝜎𝜎𝑙𝑙𝑙𝑙𝑙𝑙 = 𝜎𝜎𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐾𝐾𝑡𝑡 in which nom = the total axial load divided by the cross-section area of the
sample and Kt = theoretical stress concentration factor in the elastic range.
Stresses due to fixation
Fixated materials are limited in their movement, the material with the highest stiffness will impose its
properties upon the flexible material, since this material can not handle the expansion and shrinkage.
The expansion or shrinkage van be hampered by the resistance of fixations and underlying mass. To
𝐿𝐿0
calculate this we can combine the thermal expansion and Hooke’s law: ∆𝐿𝐿 = 𝜎𝜎 ∙ ∆𝑇𝑇 ∙ in which 𝜎𝜎 =
𝐸𝐸
𝛼𝛼 ∙ ∆𝑇𝑇 ∙ 𝐸𝐸
An occurring stress will depend on the imposed material's e-modulus. Furthermore, stony materials
brittleness is an important property to take into account since a brittle material is susceptible to
cracking.
1.7 Hardness
Lenore van Vliet - 1377892
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